Insights into the secret world of housing prices - Abhiram, Mihir, Samrit, Suzie¶

Summer 2024 Data Science Project¶

Housing prices are often looked as a black box with differing perspectives of the price determination like size of the house, location, and with some even feeling like it's completely random. We, along with a lot of people across the United States, one day envision owning homes making it important for us to get a deeper understanding of the topic. Throughout the process - from dataset collection to conclusion development - we kept in mind considerations that many people can relate to when purchasing a home such as does it feel more expensive to buy a home in summer vs winter or do homes with larger prices have lots of bathrooms. Our dataset was collected on Kaggle.com and has 19(?) features along with the target variable of price sold. We hope that one day housing prices calculations can be as simple as plugging in the values of the features and getting an exact estimate for one's house value. This would enable individuals to optimize for the factors that are the most valuable to them while staying under budget.

Data Collection¶

We are choosing the Housing Prices Dataset set from Sukhmandeep Singh Brar. This housing price dataset provides a comprehensive collection of property listings, encompassing various attributes such as the number of bedrooms, bathrooms, living area size, lot size, and zip codes, all gathered from house listings in and around Seattle. We found this dataset on Kaggle from the original author.

We’ve chosen this dataset for its large size (2.52 MB) and for the large number of features associated with each house listing, totaling 21 features for each house. It is also localized to a single area (Seattle) which will allow us to extract specific and in-depth insights

Through this dataset, we aim to analyze and determine the effect of various features such as zip code, number of floors, number of bedrooms, square footage, and more on the estimated price of a house.

We are choosing this dataset to understand and analyze which house features best predict the price and which variables affect housing prices most severely. We will leverage several techniques including regression modeling to determine the value of a house based on various input variables.

Source Dataset link: https://www.kaggle.com/datasets/sukhmandeepsinghbrar/housing-price-dataset

As our team used google colab for much of this there are some code cells that account for runs on google colab, however much of the visualization can only be done locally so these cells will be commented out when submitted

In [1]:
#for google colab
#from google.colab import drive
#drive.mount('/content/drive')

We perform all relevant imports and read in our primary dataset

In [2]:
#import
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import scipy.stats as stats
import folium
import geopandas as gpd

#make sure the csv is in your top level drive directory, if you try and put it in a subfolder then that filepath becomes invalid for the others
data = pd.read_csv('Housing.csv')
#data = pd.read_csv('/content/drive/My Drive/Housing.csv')
#data = pd.read_csv('/content/drive/My Drive/cmsc320-finalproject/Housing.csv')

Data Processing¶

Perform data cleaning and encoding of data types in incorrect/unusable formats

We also perform feature creation, it may be useful to have additional data such as the total number of rooms in a house and the price per square footage

In [3]:
data = pd.read_csv('Housing.csv')
#parse


#handling NaNs
print(data.isnull().sum())

data['bedrooms'] = data['bedrooms'].fillna(data['bedrooms'].median()) # Filling missing values
data['bathrooms'] = data['bathrooms'].fillna(data['bathrooms'].median())

data.dropna(subset=['price'], inplace=True) # Dropping rows where the 'price' is missing

data['yr_renovated'] = data['yr_renovated'].fillna(0) # Filling 'yr_renovated' with 0 where NaNs may imply no renovation


#string converts
data['date'] = pd.to_datetime(data['date'])
data['id'] = data['id'].astype(str)


#encoding
data['house_age'] = data['date'].dt.year - data['yr_built']
#should make years since renovation equal years since it was built if 0
#data['years_since_renovation'] = data.apply(lambda row: row['date'].year - row['yr_renovated'] if row['yr_renovated'] != 0 else 0, axis=1)
data['years_since_renovation'] = data.apply(
    lambda row: row['date'].year - row['yr_renovated'] if row['yr_renovated'] != 0 else row['date'].year - row['yr_built'],
    axis=1
)
#new cols
data['num_rooms'] = data['bedrooms'] + data['bathrooms']
data['living percentage'] = (data['sqft_living'])/(data['sqft_lot'])
data['price_per_sqft_living'] = data['price']/data['sqft_living']
data['price_per_sqft_lot'] = data['price']/data['sqft_lot']
id               0
date             0
price            0
bedrooms         0
bathrooms        0
sqft_living      0
sqft_lot         0
floors           0
waterfront       0
view             0
condition        0
grade            0
sqft_above       0
sqft_basement    0
yr_built         0
yr_renovated     0
zipcode          0
lat              0
long             0
sqft_living15    0
sqft_lot15       0
dtype: int64
In [4]:
# organize (sort by date)
data.sort_values(by='date', inplace=True)
data.reset_index(drop=True, inplace=True)

Exploratory Data Analysis and visualization¶

Continuous Data Analysis¶

To begin with let us look at what the columns of our imported data look like

In [5]:
#general testing
data.head(10)
Out[5]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront view ... lat long sqft_living15 sqft_lot15 house_age years_since_renovation num_rooms living percentage price_per_sqft_living price_per_sqft_lot
0 5561000190 2014-05-02 437500.0 3 2.25 1970 35100 2.0 0 0 ... 47.4635 -121.991 2340 35100 37 37 5.25 0.056125 222.081218 12.464387
1 472000620 2014-05-02 790000.0 3 2.50 2600 4750 1.0 0 0 ... 47.6833 -122.400 2380 4750 63 63 5.50 0.547368 303.846154 166.315789
2 1024069009 2014-05-02 675000.0 5 2.50 2820 67518 2.0 0 0 ... 47.5794 -122.025 2820 48351 35 35 7.50 0.041767 239.361702 9.997334
3 7853361370 2014-05-02 555000.0 4 2.50 3310 6500 2.0 0 0 ... 47.5150 -121.870 2380 5000 2 2 6.50 0.509231 167.673716 85.384615
4 5056500260 2014-05-02 440000.0 4 2.25 2160 8119 1.0 0 0 ... 47.5443 -122.177 1850 9000 48 48 6.25 0.266043 203.703704 54.193866
5 3438501320 2014-05-02 295000.0 2 2.50 1630 1368 2.0 0 0 ... 47.5489 -122.363 1590 2306 5 5 4.50 1.191520 180.981595 215.643275
6 1737320120 2014-05-02 470000.0 5 2.50 2210 9655 1.0 0 0 ... 47.7698 -122.222 2080 8633 38 38 7.50 0.228897 212.669683 48.679441
7 7197300105 2014-05-02 550000.0 4 2.50 1940 10500 1.0 0 0 ... 47.6830 -122.114 2200 10500 38 38 6.50 0.184762 283.505155 52.380952
8 1999700045 2014-05-02 313000.0 3 1.50 1340 7912 1.5 0 0 ... 47.7658 -122.339 1480 7940 59 59 4.50 0.169363 233.582090 39.560162
9 1962200037 2014-05-02 626000.0 3 2.25 1750 1572 2.5 0 0 ... 47.6498 -122.321 2410 3050 9 9 5.25 1.113232 357.714286 398.218830

10 rows × 27 columns

Mihir's Section

As we are looking to explore this data set it may be a good idea to get an idea of how all the variables are interrelated

In [6]:
#Mihir - Covariance matrix of all features
CovMatrix = data.cov()

#However correlation matrix will be more useful as it scales everything using standard deviations to between -1 to 1, makes it easier to compare between factors
CorrMatrix = data.corr(method = 'pearson')
In [7]:
#prints much better if you stick it in its own cell
data.cov()
Out[7]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront view ... lat long sqft_living15 sqft_lot15 house_age years_since_renovation num_rooms living percentage price_per_sqft_living price_per_sqft_lot
id 8.274654e+18 1.566785e+23 -1.770230e+13 3.316999e+06 1.142695e+07 -3.238863e+10 -1.574064e+13 2.877320e+07 -6.772400e+05 2.555269e+07 ... -7.539282e+05 8.425348e+06 -5.722532e+09 -1.090153e+13 -1.792808e+09 -1.434415e+09 1.474395e+07 6.806534e+07 -1.749445e+09 1.618107e+10
date 1.566785e+23 9.540109e+31 -1.562305e+19 -1.525486e+14 -2.588457e+14 -3.100206e+17 2.553979e+18 -1.186211e+14 1.145477e+12 -1.347551e+13 ... -4.446697e+13 -9.655969e+12 -2.109778e+17 6.842317e+17 3.999961e+15 7.098913e+15 -4.113943e+14 -1.267093e+13 4.081743e+16 7.885853e+15
price -1.770230e+13 -1.562305e+19 1.347821e+11 1.053004e+05 1.484810e+05 2.367150e+08 1.363432e+09 5.090779e+04 8.460640e+03 1.117729e+05 ... 1.561740e+04 1.118099e+03 1.472961e+08 8.264560e+08 -5.818276e+05 -1.117816e+06 2.537814e+05 1.213879e+04 2.241334e+07 1.063007e+07
bedrooms 3.316999e+06 -1.525486e+14 1.053004e+05 8.650956e-01 3.695787e-01 4.926377e+02 1.221762e+03 8.812733e-02 -5.293190e-04 5.669500e-02 ... -1.148704e-03 1.696024e-02 2.496817e+02 7.429740e+02 -4.217009e+00 -4.439367e+00 1.234674e+00 6.658814e-03 -2.109089e+01 -5.451275e+00
bathrooms 1.142695e+07 -2.588457e+14 1.484810e+05 3.695787e-01 5.931513e-01 5.338120e+02 2.798944e+03 2.082114e-01 4.247388e-03 1.108004e-01 ... 2.622344e-03 2.419130e-02 3.001611e+02 1.833182e+03 -1.145691e+01 -1.192709e+01 9.627300e-01 5.922581e-02 -7.749677e+00 1.464115e+01
sqft_living -3.238863e+10 -3.100206e+17 2.367150e+08 4.926377e+02 5.338120e+02 8.435337e+05 6.574684e+06 1.755404e+02 8.249461e+00 2.003143e+02 ... 6.685035e+00 3.107108e+01 4.761601e+05 4.596302e+06 -8.592709e+03 -9.107057e+03 1.026450e+03 1.904793e+01 -9.331851e+03 1.947152e+03
sqft_lot -1.574064e+13 2.553979e+18 1.363432e+09 1.221762e+03 2.798944e+03 6.574684e+06 1.715659e+09 -1.163286e+02 7.741867e+01 2.371393e+03 ... -4.917661e+02 1.338837e+03 4.105319e+06 8.126540e+08 -6.447493e+04 -6.302673e+04 4.020705e+03 -2.811031e+03 -1.541897e+05 -8.039670e+05
floors 2.877320e+07 -1.186211e+14 5.090779e+04 8.812733e-02 2.082114e-01 1.755404e+02 -1.163286e+02 2.915880e-01 1.107146e-03 1.218394e-02 ... 3.712271e-03 9.537583e-03 1.035866e+02 -1.661524e+02 -7.766885e+00 -7.867447e+00 2.963387e-01 8.078183e-02 2.280253e-01 2.428315e+01
waterfront -6.772400e+05 1.145477e+12 8.460640e+03 -5.293190e-04 4.247388e-03 8.249461e+00 7.741867e+01 1.107146e-03 7.485226e-03 2.664300e-02 ... -1.711161e-04 -5.106370e-04 5.127103e+00 7.252979e+01 6.631481e-02 1.169693e-03 3.718069e-03 -6.941712e-04 1.839817e+00 2.490478e-01
view 2.555269e+07 -1.347551e+13 1.117729e+05 5.669500e-02 1.108004e-01 2.003143e+02 2.371393e+03 1.218394e-02 2.664300e-02 5.872426e-01 ... 6.537452e-04 -8.460837e-03 1.472943e+02 1.518526e+03 1.203386e+00 4.036811e-01 1.674954e-01 -2.690266e-04 1.863367e+01 5.681183e+00
condition -4.452067e+07 -3.226869e+14 8.686852e+03 1.725115e-02 -6.263824e-02 -3.511460e+01 -2.414616e+02 -9.268648e-02 9.375805e-04 2.293397e-02 ... -1.347221e-03 -9.760027e-03 -4.140089e+01 -6.050935e+01 6.894440e+00 7.416206e+00 -4.538708e-02 -2.727252e-02 7.329965e+00 -5.252303e+00
grade 2.748834e+07 -4.582380e+14 2.880262e+05 3.902840e-01 6.020054e-01 8.234077e+02 5.531997e+03 2.908243e-01 8.417993e-03 2.263832e-01 ... 1.858155e-02 3.283811e-02 5.745907e+02 3.827254e+03 -1.544911e+01 -1.561983e+01 9.922894e-01 6.053961e-02 1.588124e+01 2.412967e+01
sqft_above -2.582941e+10 -2.258601e+17 1.841011e+08 3.678642e+02 4.370876e+02 6.666978e+05 6.294462e+06 2.342603e+02 5.163720e+00 1.063870e+02 ... -9.368779e-02 4.009385e+01 4.153850e+05 4.387534e+06 -1.032007e+04 -1.040758e+04 8.049518e+02 1.154410e+01 -8.076881e+03 -3.563238e+02
sqft_basement -6.559226e+09 -8.416047e+16 5.261393e+07 1.247734e+02 9.672443e+01 1.768358e+05 2.802218e+05 -5.871985e+01 3.085741e+00 9.392727e+01 ... 6.778723e+00 -9.022770e+00 6.077510e+04 2.087679e+05 1.727359e+03 1.300528e+03 2.214979e+02 7.503838e+00 -1.254971e+03 2.303476e+03
yr_built 1.806430e+09 -1.019331e+14 5.824414e+05 4.212745e+00 1.144733e+01 8.580238e+03 6.458085e+04 7.761250e+00 -6.648330e-02 -1.202897e+00 ... -6.028713e-01 1.693346e+00 6.567732e+03 5.690946e+04 -8.627491e+02 -7.698889e+02 1.566008e+01 2.202409e+00 -9.371025e+02 3.442951e+02
yr_renovated -1.953565e+10 -9.615773e+16 1.864482e+07 7.042583e+00 1.569654e+01 2.042442e+04 1.271708e+05 1.374814e+00 3.227949e+00 3.198718e+01 ... 1.636217e+00 -3.867676e+00 -7.357744e+02 8.613634e+04 2.648760e+03 -1.908793e+03 2.273912e+01 -3.664272e-01 4.663262e+03 1.399137e+03
zipcode -1.265349e+09 7.335453e+14 -1.045028e+06 -7.601869e+00 -8.400840e+00 -9.800232e+03 -2.871637e+05 -1.708121e+00 1.401912e-01 3.478060e+00 ... 1.979855e+00 -4.250293e+00 -1.023266e+04 -2.150769e+05 5.451781e+02 4.942046e+02 -1.600271e+01 2.555770e+00 1.016621e+03 1.115758e+03
lat -7.539282e+05 -4.446697e+13 1.561740e+04 -1.148704e-03 2.622344e-03 6.685035e+00 -4.917661e+02 3.712271e-03 -1.711161e-04 6.537452e-04 ... 1.919990e-02 -2.644336e-03 4.640056e+00 -3.269542e+02 6.009785e-01 5.391607e-01 1.473640e-03 6.138167e-03 7.198930e+00 3.791880e+00
long 8.425348e+06 -9.655969e+12 1.118099e+03 1.696024e-02 2.419130e-02 3.107108e+01 1.338837e+03 9.537583e-03 -5.106370e-04 -8.460837e-03 ... -2.644336e-03 1.983262e-02 3.229692e+01 9.784167e+02 -1.693329e+00 -1.553609e+00 4.115154e-02 -7.729806e-03 -3.658430e+00 -3.569414e+00
sqft_living15 -5.722532e+09 -2.109778e+17 1.472961e+08 2.496817e+02 3.001611e+02 4.761601e+05 4.105319e+06 1.035866e+02 5.127103e+00 1.472943e+02 ... 4.640056e+00 3.229692e+01 4.697612e+05 3.428259e+06 -6.574697e+03 -6.415450e+03 5.498428e+02 -7.755340e+00 2.908721e+03 -2.867380e+03
sqft_lot15 -1.090153e+13 6.842317e+17 8.264560e+08 7.429740e+02 1.833182e+03 4.596302e+06 8.126540e+08 -1.661524e+02 7.252979e+01 1.518526e+03 ... -3.269542e+02 9.784167e+02 3.428259e+06 7.455182e+08 -5.691054e+04 -5.523156e+04 2.576156e+03 -2.034166e+03 -1.728430e+05 -5.873583e+05
house_age -1.792808e+09 3.999961e+15 -5.818276e+05 -4.217009e+00 -1.145691e+01 -8.592709e+03 -6.447493e+04 -7.766885e+00 6.631481e-02 1.203386e+00 ... 6.009785e-01 -1.693329e+00 -6.574697e+03 -5.691054e+04 8.629196e+02 7.701938e+02 -1.567392e+01 -2.203452e+00 9.394453e+02 -3.438461e+02
years_since_renovation -1.434415e+09 7.098913e+15 -1.117816e+06 -4.439367e+00 -1.192709e+01 -9.107057e+03 -6.302673e+04 -7.867447e+00 1.169693e-03 4.036811e-01 ... 5.391607e-01 -1.553609e+00 -6.415450e+03 -5.523156e+04 7.701938e+02 8.302260e+02 -1.636646e+01 -2.294506e+00 7.924248e+02 -4.208357e+02
num_rooms 1.474395e+07 -4.113943e+14 2.537814e+05 1.234674e+00 9.627300e-01 1.026450e+03 4.020705e+03 2.963387e-01 3.718069e-03 1.674954e-01 ... 1.473640e-03 4.115154e-02 5.498428e+02 2.576156e+03 -1.567392e+01 -1.636646e+01 2.197404e+00 6.588463e-02 -2.884057e+01 9.189874e+00
living percentage 6.806534e+07 -1.267093e+13 1.213879e+04 6.658814e-03 5.922581e-02 1.904793e+01 -2.811031e+03 8.078183e-02 -6.941712e-04 -2.690266e-04 ... 6.138167e-03 -7.729806e-03 -7.755340e+00 -2.034166e+03 -2.203452e+00 -2.294506e+00 6.588463e-02 7.212734e-02 3.447523e+00 2.263822e+01
price_per_sqft_living -1.749445e+09 4.081743e+16 2.241334e+07 -2.109089e+01 -7.749677e+00 -9.331851e+03 -1.541897e+05 2.280253e-01 1.839817e+00 1.863367e+01 ... 7.198930e+00 -3.658430e+00 2.908721e+03 -1.728430e+05 9.394453e+02 7.924248e+02 -2.884057e+01 3.447523e+00 1.211332e+04 4.663091e+03
price_per_sqft_lot 1.618107e+10 7.885853e+15 1.063007e+07 -5.451275e+00 1.464115e+01 1.947152e+03 -8.039670e+05 2.428315e+01 2.490478e-01 5.681183e+00 ... 3.791880e+00 -3.569414e+00 -2.867380e+03 -5.873583e+05 -3.438461e+02 -4.208357e+02 9.189874e+00 2.263822e+01 4.663091e+03 8.846382e+03

27 rows × 27 columns

However the correlation matrix will be more useful as it scales everything using standard deviations to between -1 to 1, makes it easier to compare between factors

In [8]:
data.corr(method = 'pearson')
Out[8]:
id date price bedrooms bathrooms sqft_living sqft_lot floors waterfront view ... lat long sqft_living15 sqft_lot15 house_age years_since_renovation num_rooms living percentage price_per_sqft_living price_per_sqft_lot
id 1.000000 0.005576 -0.016762 0.001240 0.005158 -0.012259 -0.132109 0.018524 -0.002721 0.011592 ... -0.001891 0.020798 -0.002903 -0.138798 -0.021216 -0.017306 0.003458 0.088105 -0.005526 0.059807
date 0.005576 1.000000 -0.004357 -0.016792 -0.034410 -0.034559 0.006313 -0.022491 0.001356 -0.001800 ... -0.032856 -0.007020 -0.031515 0.002566 0.013941 0.025224 -0.028414 -0.004830 0.037970 0.008584
price -0.016762 -0.004357 1.000000 0.308377 0.525136 0.702035 0.089661 0.256793 0.266370 0.397294 ... 0.307003 0.021626 0.585378 0.082447 -0.053950 -0.105671 0.466325 0.123115 0.554701 0.307848
bedrooms 0.001240 -0.016792 0.308377 1.000000 0.515932 0.576693 0.031713 0.175466 -0.006578 0.079543 ... -0.008913 0.129482 0.391666 0.029256 -0.154343 -0.165650 0.895500 0.026657 -0.206030 -0.062314
bathrooms 0.005158 -0.034410 0.525136 0.515932 1.000000 0.754665 0.087740 0.500653 0.063744 0.187737 ... 0.024573 0.223042 0.568634 0.087175 -0.506407 -0.537469 0.843270 0.286338 -0.091426 0.202120
sqft_living -0.012259 -0.034559 0.702035 0.576693 0.754665 1.000000 0.172826 0.353949 0.103818 0.284611 ... 0.052529 0.240223 0.756420 0.183286 -0.318488 -0.344135 0.753931 0.077223 -0.092318 0.022541
sqft_lot -0.132109 0.006313 0.089661 0.031713 0.087740 0.172826 1.000000 -0.005201 0.021604 0.074710 ... -0.085683 0.229521 0.144608 0.718557 -0.052990 -0.052809 0.065483 -0.252697 -0.033823 -0.206367
floors 0.018524 -0.022491 0.256793 0.175466 0.500653 0.353949 -0.005201 1.000000 0.023698 0.029444 ... 0.049614 0.125419 0.279885 -0.011269 -0.489640 -0.505651 0.370210 0.557030 0.003837 0.478120
waterfront -0.002721 0.001356 0.266370 -0.006578 0.063744 0.103818 0.021604 0.023698 1.000000 0.401857 ... -0.014274 -0.041910 0.086463 0.030703 0.026093 0.000469 0.028991 -0.029875 0.193215 0.030605
view 0.011592 -0.001800 0.397294 0.079543 0.187737 0.284611 0.074710 0.029444 0.401857 1.000000 ... 0.006157 -0.078400 0.280439 0.072575 0.053458 0.018282 0.147448 -0.001307 0.220932 0.078822
condition -0.023784 -0.050769 0.036361 0.028502 -0.124982 -0.058753 -0.008958 -0.263768 0.016653 0.045990 ... -0.014941 -0.106500 -0.092824 -0.003406 0.360665 0.395525 -0.047051 -0.156051 0.102344 -0.085814
grade 0.008130 -0.039912 0.667434 0.356978 0.664983 0.762704 0.113621 0.458183 0.082775 0.251321 ... 0.114084 0.198372 0.713202 0.119248 -0.447415 -0.461180 0.569477 0.191771 0.122757 0.218253
sqft_above -0.010843 -0.027924 0.605567 0.477614 0.685342 0.876597 0.183512 0.523885 0.072075 0.167649 ... -0.000816 0.343803 0.731870 0.194050 -0.424248 -0.436188 0.655748 0.051908 -0.088620 -0.004575
sqft_basement -0.005152 -0.019469 0.323816 0.303112 0.283770 0.435043 0.015286 -0.245705 0.080588 0.276947 ... 0.110538 -0.144765 0.200355 0.017276 0.132865 0.101985 0.337620 0.063132 -0.025764 0.055337
yr_built 0.021379 -0.000355 0.054011 0.154198 0.506019 0.318049 0.053080 0.489319 -0.026161 -0.053440 ... -0.148122 0.409356 0.326229 0.070958 -0.999873 -0.909652 0.359654 0.279186 -0.289869 0.124622
yr_renovated -0.016907 -0.024509 0.126434 0.018850 0.050739 0.055363 0.007644 0.006338 0.092885 0.103917 ... 0.029398 -0.068372 -0.002673 0.007854 0.224480 -0.164923 0.038189 -0.003397 0.105482 0.037034
zipcode -0.008221 0.001404 -0.053201 -0.152754 -0.203866 -0.199430 -0.129574 -0.059121 0.030285 0.084827 ... 0.267048 -0.564072 -0.279033 -0.147221 0.346864 0.320563 -0.201764 0.177860 0.172637 0.221714
lat -0.001891 -0.032856 0.307003 -0.008913 0.024573 0.052529 -0.085683 0.049614 -0.014274 0.006157 ... 1.000000 -0.135512 0.048858 -0.086419 0.147647 0.135043 0.007174 0.164945 0.472049 0.290953
long 0.020798 -0.007020 0.021626 0.129482 0.223042 0.240223 0.229521 0.125419 -0.041910 -0.078400 ... -0.135512 1.000000 0.334605 0.254451 -0.409323 -0.382872 0.197125 -0.204375 -0.236033 -0.269478
sqft_living15 -0.002903 -0.031515 0.585378 0.391666 0.568634 0.756420 0.144608 0.279885 0.086463 0.280439 ... 0.048858 0.334605 1.000000 0.183192 -0.326552 -0.324856 0.541184 -0.042132 0.038560 -0.044480
sqft_lot15 -0.138798 0.002566 0.082447 0.029256 0.087175 0.183286 0.718557 -0.011269 0.030703 0.072575 ... -0.086419 0.254451 0.183192 1.000000 -0.070954 -0.070204 0.063648 -0.277401 -0.057516 -0.228713
house_age -0.021216 0.013941 -0.053950 -0.154343 -0.506407 -0.318488 -0.052990 -0.489640 0.026093 0.053458 ... 0.147647 -0.409323 -0.326552 -0.070954 1.000000 0.909948 -0.359946 -0.279298 0.290573 -0.124450
years_since_renovation -0.017306 0.025224 -0.105671 -0.165650 -0.537469 -0.344135 -0.052809 -0.505651 0.000469 0.018282 ... 0.135043 -0.382872 -0.324856 -0.070204 0.909948 1.000000 -0.383179 -0.296511 0.249878 -0.155286
num_rooms 0.003458 -0.028414 0.466325 0.895500 0.843270 0.753931 0.065483 0.370210 0.028991 0.147448 ... 0.007174 0.197125 0.541184 0.063648 -0.359946 -0.383179 1.000000 0.165493 -0.176774 0.065913
living percentage 0.088105 -0.004830 0.123115 0.026657 0.286338 0.077223 -0.252697 0.557030 -0.029875 -0.001307 ... 0.164945 -0.204375 -0.042132 -0.277401 -0.279298 -0.296511 0.165493 1.000000 0.116634 0.896209
price_per_sqft_living -0.005526 0.037970 0.554701 -0.206030 -0.091426 -0.092318 -0.033823 0.003837 0.193215 0.220932 ... 0.472049 -0.236033 0.038560 -0.057516 0.290573 0.249878 -0.176774 0.116634 1.000000 0.450463
price_per_sqft_lot 0.059807 0.008584 0.307848 -0.062314 0.202120 0.022541 -0.206367 0.478120 0.030605 0.078822 ... 0.290953 -0.269478 -0.044480 -0.228713 -0.124450 -0.155286 0.065913 0.896209 0.450463 1.000000

27 rows × 27 columns

As our ultimate goal is to predict the price of a house based on its feature, the most relevant column of this matrix is of the price

In [9]:
#correlations of price with all other current variables
print(CorrMatrix['price'])
id                       -0.016762
date                     -0.004357
price                     1.000000
bedrooms                  0.308377
bathrooms                 0.525136
sqft_living               0.702035
sqft_lot                  0.089661
floors                    0.256793
waterfront                0.266370
view                      0.397294
condition                 0.036361
grade                     0.667434
sqft_above                0.605567
sqft_basement             0.323816
yr_built                  0.054011
yr_renovated              0.126434
zipcode                  -0.053201
lat                       0.307003
long                      0.021626
sqft_living15             0.585378
sqft_lot15                0.082447
house_age                -0.053950
years_since_renovation   -0.105671
num_rooms                 0.466325
living percentage         0.123115
price_per_sqft_living     0.554701
price_per_sqft_lot        0.307848
Name: price, dtype: float64

As we can see the grading system that has been used by the realtors is quite good and is fairly correlated with price, another factor that is hugely correlated with price is square footage, which is why it may be better to explore price per square footage to gain insight into what nontrivial qualities affect the price of a house

In [10]:
print(CorrMatrix['price_per_sqft_living'])
id                       -0.005526
date                      0.037970
price                     0.554701
bedrooms                 -0.206030
bathrooms                -0.091426
sqft_living              -0.092318
sqft_lot                 -0.033823
floors                    0.003837
waterfront                0.193215
view                      0.220932
condition                 0.102344
grade                     0.122757
sqft_above               -0.088620
sqft_basement            -0.025764
yr_built                 -0.289869
yr_renovated              0.105482
zipcode                   0.172637
lat                       0.472049
long                     -0.236033
sqft_living15             0.038560
sqft_lot15               -0.057516
house_age                 0.290573
years_since_renovation    0.249878
num_rooms                -0.176774
living percentage         0.116634
price_per_sqft_living     1.000000
price_per_sqft_lot        0.450463
Name: price_per_sqft_living, dtype: float64

We can also find all other correlations that may be of interest by printing those above a certain R^2 value

In [11]:
#finding all other correlations that may be of interest
correlationThreshold = 0.3
checkedList = []

for row in CorrMatrix.index:
  for col in CorrMatrix.columns:
    if (not row in checkedList) and (not col in checkedList) and (row != col) and (CorrMatrix[row][col] > correlationThreshold or CorrMatrix[row][col] < -correlationThreshold):
      print(row, col, CorrMatrix[row][col])
  checkedList.append(row)
price bedrooms 0.3083769180156153
price bathrooms 0.5251363218554719
price sqft_living 0.7020346040056666
price view 0.39729352797680806
price grade 0.6674342691668146
price sqft_above 0.6055670405615354
price sqft_basement 0.3238155679576574
price lat 0.3070033728790943
price sqft_living15 0.5853783781780082
price num_rooms 0.4663250127585262
price price_per_sqft_living 0.5547008682090738
price price_per_sqft_lot 0.30784846349389644
bedrooms bathrooms 0.5159316152210395
bedrooms sqft_living 0.57669257587632
bedrooms grade 0.3569778987944419
bedrooms sqft_above 0.47761446504670363
bedrooms sqft_basement 0.30311202501453155
bedrooms sqft_living15 0.39166621103010474
bedrooms num_rooms 0.8954995511941201
bathrooms sqft_living 0.7546652789673763
bathrooms floors 0.5006531725878747
bathrooms grade 0.664982533878076
bathrooms sqft_above 0.6853424758761565
bathrooms yr_built 0.5060194382852586
bathrooms sqft_living15 0.5686342895782276
bathrooms house_age -0.5064069441397088
bathrooms years_since_renovation -0.537469341028698
bathrooms num_rooms 0.8432702460643129
sqft_living floors 0.35394929023671473
sqft_living grade 0.7627044764584723
sqft_living sqft_above 0.8765965986813177
sqft_living sqft_basement 0.4350429736698242
sqft_living yr_built 0.3180487689964427
sqft_living sqft_living15 0.7564202590172292
sqft_living house_age -0.31848847620130405
sqft_living years_since_renovation -0.3441348746046749
sqft_living num_rooms 0.7539307566069245
sqft_lot sqft_lot15 0.7185567524330329
floors grade 0.45818251367194757
floors sqft_above 0.5238847102851497
floors yr_built 0.48931942474365014
floors house_age -0.48963996546979405
floors years_since_renovation -0.505650922321103
floors num_rooms 0.37021041036533103
floors living percentage 0.5570303807316453
floors price_per_sqft_lot 0.4781204780795243
waterfront view 0.4018573506975677
condition yr_built -0.36141656224866653
condition house_age 0.3606652284795277
condition years_since_renovation 0.39552514408825024
grade sqft_above 0.7559229376236478
grade yr_built 0.4469632049266092
grade sqft_living15 0.7132020930151758
grade house_age -0.4474152409756253
grade years_since_renovation -0.46118017003453
grade num_rooms 0.5694767212967314
sqft_above yr_built 0.423898351663744
sqft_above long 0.3438030174605131
sqft_above sqft_living15 0.7318702923539874
sqft_above house_age -0.4242475329942809
sqft_above years_since_renovation -0.4361880253823974
sqft_above num_rooms 0.6557477942021749
sqft_basement num_rooms 0.337619598952765
yr_built zipcode -0.3468691778552612
yr_built long 0.4093562026388897
yr_built sqft_living15 0.3262288995957142
yr_built house_age -0.9998732929914715
yr_built years_since_renovation -0.9096524794041762
yr_built num_rooms 0.3596537193321721
zipcode long -0.564071606442267
zipcode house_age 0.34686352751305144
zipcode years_since_renovation 0.32056344232979844
lat price_per_sqft_living 0.47204862811027676
long sqft_living15 0.33460498382715503
long house_age -0.4093228953977021
long years_since_renovation -0.3828719068575162
sqft_living15 house_age -0.3265517538903627
sqft_living15 years_since_renovation -0.32485560112321155
sqft_living15 num_rooms 0.5411840225422982
house_age years_since_renovation 0.9099482701339621
house_age num_rooms -0.3599461100668001
years_since_renovation num_rooms -0.3831789177472444
living percentage price_per_sqft_lot 0.89620946404785
price_per_sqft_living price_per_sqft_lot 0.4504632365624928

This creates a heatmap of all the houses so we can visualize all areas of interest that will be covered by our dataset

In [12]:
houses_map = folium.Map(location=[data['lat'].mean(), data['long'].mean()], zoom_start=10)

for _, row in data.iterrows():
    folium.Marker(
        [row['lat'], row['long']]
    ).add_to(houses_map)

houses_map.save('AllHouseLocations.html')

from folium.plugins import HeatMap
houses_heatmap = folium.Map(location=[data['lat'].mean(), data['long'].mean()], zoom_start=10)
heat_data = data[['lat', 'long']].values.tolist()
HeatMap(heat_data).add_to(houses_heatmap)
houses_heatmap.save('AllHouseLocationsHeatmap.html')

houses_heatmap
Out[12]:
Make this Notebook Trusted to load map: File -> Trust Notebook

As we can see we cover most of the Seattle area, but not Seattle itself

Boolean/Categorical Data Analysis¶

First, we calculate summary statistics for categorical features such as 'waterfront', 'view', 'condition', 'grade', and 'floors'. This helps us understand the distribution and typical values of these categorical variables.

In [13]:
# Analysis on boolean/categorical data (waterfront, view, condition, grade, floors)
def calculate_summary_statistics(data, column_name):
    count = data[column_name].count()  # Count non-null entries
    mean = data[column_name].mean()  # Mean
    std = data[column_name].std()  # Standard deviation
    min_val = data[column_name].min()  # Minimum value
    q25 = data[column_name].quantile(0.25)  # 25th percentile
    median = data[column_name].median()  # Median
    q75 = data[column_name].quantile(0.75)  # 75th percentile
    max_val = data[column_name].max()  # Maximum value

    return {
        "Count": count,
        "Mean": mean,
        "Standard Deviation": std,
        "Min": min_val,
        "25th Percentile": q25,
        "50th Percentile (Median)": median,
        "75th Percentile": q75,
        "Max": max_val
    }

columns_to_analyze = ['waterfront', 'view', 'condition', 'grade', 'floors']

# Calculating and displaying summary statistics for each column
summary_statistics = {}
for column in columns_to_analyze:
    summary_statistics[column] = calculate_summary_statistics(data, column)

summary_statistics
Out[13]:
{'waterfront': {'Count': 21613,
  'Mean': 0.007541757275713691,
  'Standard Deviation': 0.08651719772790183,
  'Min': 0,
  '25th Percentile': 0.0,
  '50th Percentile (Median)': 0.0,
  '75th Percentile': 0.0,
  'Max': 1},
 'view': {'Count': 21613,
  'Mean': 0.23430342849211122,
  'Standard Deviation': 0.7663175692736391,
  'Min': 0,
  '25th Percentile': 0.0,
  '50th Percentile (Median)': 0.0,
  '75th Percentile': 0.0,
  'Max': 4},
 'condition': {'Count': 21613,
  'Mean': 3.4094295100171195,
  'Standard Deviation': 0.6507430463662562,
  'Min': 1,
  '25th Percentile': 3.0,
  '50th Percentile (Median)': 3.0,
  '75th Percentile': 4.0,
  'Max': 5},
 'grade': {'Count': 21613,
  'Mean': 7.656873178179799,
  'Standard Deviation': 1.1754587569743047,
  'Min': 1,
  '25th Percentile': 7.0,
  '50th Percentile (Median)': 7.0,
  '75th Percentile': 8.0,
  'Max': 13},
 'floors': {'Count': 21613,
  'Mean': 1.4943089807060566,
  'Standard Deviation': 0.5399888951423845,
  'Min': 1.0,
  '25th Percentile': 1.0,
  '50th Percentile (Median)': 1.5,
  '75th Percentile': 2.0,
  'Max': 3.5}}

Chi-Square Test for Independence Between Categorical Variables¶

Next, we perform Chi-square tests to examine the independence between pairs of categorical variables. This statistical test helps us understand if there are significant associations between different property characteristics.

In [14]:
# Chi-Square Test to waterfront and view, waterfront and condition, view and condition, condition and grade, grade and floors

from scipy.stats import chi2_contingency

def chi_square_test(data, var1, var2):
    contingency_table = pd.crosstab(data[var1], data[var2])
    chi2, p, dof, expected = chi2_contingency(contingency_table)
    return chi2, p, dof, expected

# Pairs of variables to test
variable_pairs = [
    ('waterfront', 'view'),
    ('waterfront', 'condition'),
    ('view', 'condition'),
    ('condition', 'grade'),
    ('grade', 'floors')
]

# Performing Chi-Square Tests
chi_square_results = {}
for var1, var2 in variable_pairs:
    chi2, p, dof, expected = chi_square_test(data, var1, var2)
    chi_square_results[(var1, var2)] = {'chi2': chi2, 'p-value': p, 'dof': dof, 'expected': expected}

chi_square_results


# Interpretation:
# Waterfront vs. View: The p-value is 0.0, which is less than 0.05, indicating that there is a significant association between the waterfront status and the view rating.
# Waterfront vs. Condition: The p-value is 0.039, which is less than 0.05, indicating that there is a significant association between the waterfront status and the condition of the house.
# View vs. Condition: The p-value is extremely low (1.82e-08), indicating a significant association between the view rating and the condition of the house.
# Condition vs. Grade: The p-value is 0.0, which is less than 0.05, indicating a significant association between the condition of the house and its grade.
# Grade vs. Floors: The p-value is 0.0, which is less than 0.05, indicating a significant association between the grade of the house and the number of floors.
Out[14]:
{('waterfront', 'view'): {'chi2': 7572.5563318397735,
  'p-value': 0.0,
  'dof': 4,
  'expected': array([[1.93420187e+04, 3.29496137e+02, 9.55737288e+02, 5.06153704e+02,
          3.16594179e+02],
         [1.46981308e+02, 2.50386342e+00, 7.26271226e+00, 3.84629621e+00,
          2.40582057e+00]])},
 ('waterfront', 'condition'): {'chi2': 10.074729585287205,
  'p-value': 0.03918751144589182,
  'dof': 4,
  'expected': array([[2.97737473e+01, 1.70702818e+02, 1.39251816e+04, 5.63617036e+03,
          1.68817147e+03],
         [2.26252718e-01, 1.29718225e+00, 1.05818396e+02, 4.28296396e+01,
          1.28285291e+01]])},
 ('view', 'condition'): {'chi2': 68.50224408217254,
  'p-value': 1.822893843270391e-08,
  'dof': 16,
  'expected': array([[2.70517744e+01, 1.55096840e+02, 1.26521149e+04, 5.12090089e+03,
          1.53383561e+03],
         [4.60833757e-01, 2.64211354e+00, 2.15531948e+02, 8.72358303e+01,
          2.61292740e+01],
         [1.33669551e+00, 7.66372091e+00, 6.25172489e+02, 2.53036460e+02,
          7.57906353e+01],
         [7.07907278e-01, 4.05866839e+00, 3.31088234e+02, 1.34006848e+02,
          4.01383427e+01],
         [4.42789062e-01, 2.53865729e+00, 2.07092444e+02, 8.38199695e+01,
          2.51061398e+01]])},
 ('condition', 'grade'): {'chi2': 2225.6248376517715,
  'p-value': 0.0,
  'dof': 44,
  'expected': array([[1.38805349e-03, 4.16416046e-03, 4.02535511e-02, 3.35908944e-01,
          2.82885301e+00, 1.24661084e+01, 8.42270856e+00, 3.62975987e+00,
          1.57405265e+00, 5.53833341e-01, 1.24924814e-01, 1.80446953e-02],
         [7.95817332e-03, 2.38745200e-02, 2.30787026e-01, 1.92587794e+00,
          1.62187572e+01, 7.14723546e+01, 4.82901957e+01, 2.08106232e+01,
          9.02456855e+00, 3.17531116e+00, 7.16235599e-01, 1.03456253e-01],
         [6.49192616e-01, 1.94757785e+00, 1.88265859e+01, 1.57104613e+02,
          1.32305455e+03, 5.83039888e+03, 3.93930079e+03, 1.69763869e+03,
          7.36184426e+02, 2.59027854e+02, 5.84273354e+01, 8.43950400e+00],
         [2.62758525e-01, 7.88275575e-01, 7.61999722e+00, 6.35875630e+01,
          5.35501874e+02, 2.35983431e+03, 1.59441873e+03, 6.87113543e+02,
          2.97968167e+02, 1.04840651e+02, 2.36482672e+01, 3.41586082e+00],
         [7.87026327e-02, 2.36107898e-01, 2.28237635e+00, 1.90460371e+01,
          1.60395965e+02, 7.06828344e+02, 4.77567575e+02, 2.05807384e+02,
          8.92487855e+01, 3.14023504e+01, 7.08323694e+00, 1.02313422e+00]])},
 ('grade', 'floors'): {'chi2': 6505.2900602236405,
  'p-value': 0.0,
  'dof': 55,
  'expected': array([[4.94147041e-01, 8.83727386e-02, 3.81298293e-01, 7.44922038e-03,
          2.83625596e-02, 3.70147596e-04],
         [1.48244112e+00, 2.65118216e-01, 1.14389488e+00, 2.23476611e-02,
          8.50876787e-02, 1.11044279e-03],
         [1.43302642e+01, 2.56280942e+00, 1.10576505e+01, 2.16027391e-01,
          8.22514228e-01, 1.07342803e-02],
         [1.19583584e+02, 2.13862027e+01, 9.22741868e+01, 1.80271133e+00,
          6.86373942e+00, 8.95757183e-02],
         [1.00707167e+03, 1.80103641e+02, 7.77085921e+02, 1.51815111e+01,
          5.78028964e+01, 7.54360801e-01],
         [4.43793458e+03, 7.93675566e+02, 3.42443997e+03, 6.69014482e+01,
          2.54724148e+02, 3.32429556e+00],
         [2.99848425e+03, 5.36245778e+02, 2.31371804e+03, 4.52018692e+01,
          1.72104011e+02, 2.24605561e+00],
         [1.29219451e+03, 2.31094712e+02, 9.97095035e+02, 1.94797113e+01,
          7.41680933e+01, 9.67935964e-01],
         [5.60362745e+02, 1.00214686e+02, 4.32392264e+02, 8.44741591e+00,
          3.21631426e+01, 4.19747374e-01],
         [1.97164669e+02, 3.52607227e+01, 1.52138019e+02, 2.97223893e+00,
          1.13166613e+01, 1.47688891e-01],
         [4.44732337e+01, 7.95354648e+00, 3.43168463e+01, 6.70429834e-01,
          2.55263036e+00, 3.33132837e-02],
         [6.42391153e+00, 1.14884560e+00, 4.95687781e+00, 9.68398649e-02,
          3.68713274e-01, 4.81191875e-03]])}}

T-Test for Difference in House Prices: With vs. Without Basement¶

We conduct a t-test to determine if there is a significant difference in the prices of houses with basements versus those without.

In [15]:
# Susie - Test if the mean price of houses with a basement is significantly different from those without a basement
from scipy.stats import ttest_ind

# Split data based on houses with/without basement
with_basement = data[data['sqft_basement'] > 0]
without_basement = data[data['sqft_basement'] == 0]

# Performing a t-test
t_stat, p_val = ttest_ind(with_basement['price'], without_basement['price'])

print(f"T-statistic: {t_stat}, P-value: {p_val}")

# Visualization
plt.figure(figsize=(10, 6))
sns.boxplot(x='sqft_basement', y='price', data=data.assign(sqft_basement=data['sqft_basement']>0))
plt.title('Price Distribution With vs. Without Basement')
plt.xlabel('Has Basement')
plt.ylabel('Price')
plt.show()
T-statistic: 26.93602313477148, P-value: 3.266907478647668e-157

Zipcode Analysis¶

As realtors often like to say, housing is all about location, location, location. And with the data we have on zipcodes we can see if this is really true. We can also scrape data externally to see what confounders, if any predict why a zip code may have more or less expensive houses (average income in a zip code, certain zipcodes being near the waterfront, etc.)

Most expensive vs. least expensive zipcodes

In [16]:
zipcode_df = data.groupby('zipcode').agg(
    avg_price=('price', 'mean'),
    avg_price_per_sqft=('price_per_sqft_living', 'mean'),
    avg_sqft_living = ('sqft_living', 'mean'),
    avg_sqft_lot = ('sqft_lot', 'mean'),
    avg_age = ('house_age','mean'),
    total_houses=('zipcode', 'size')
).reset_index()
zipcode_df
Out[16]:
zipcode avg_price avg_price_per_sqft avg_sqft_living avg_sqft_lot avg_age total_houses
0 98001 2.808047e+05 151.387938 1900.856354 14937.450276 33.643646 362
1 98002 2.342840e+05 151.174091 1627.743719 7517.633166 46.562814 199
2 98003 2.941113e+05 157.113414 1928.882143 10603.096429 37.457143 280
3 98004 1.355927e+06 475.435611 2909.022082 13104.220820 42.867508 317
4 98005 8.101649e+05 314.929231 2656.803571 19928.785714 44.553571 168
... ... ... ... ... ... ... ...
65 98177 6.761854e+05 292.918745 2323.333333 11904.403922 53.447059 255
66 98178 3.106486e+05 189.202933 1729.351145 8309.122137 59.061069 262
67 98188 2.890783e+05 169.007306 1802.772059 10126.080882 48.882353 136
68 98198 3.028789e+05 178.428610 1745.360714 10525.978571 47.614286 280
69 98199 7.918208e+05 376.546345 2161.798107 5436.283912 57.798107 317

70 rows × 7 columns

In [17]:
plt.figure(figsize=(14, 8))
sns.boxplot(x='zipcode', y='price', data=data)
plt.xticks(rotation=90)
plt.title('Price Distribution by Zip Code')
plt.xlabel('Zip Code')
plt.ylabel('Price')
plt.show()

Let's see if there are any other variables we can check that may be spatially similar and may be confounding our analysis of the price in different zip codes, for example Average house age per zipcode.

In [18]:
zipcode_df["house_age"] = data.groupby("zipcode").apply(lambda x: x["house_age"].mean()).sort_values(ascending=False)
zipcode_df.corr(method="pearson")
Out[18]:
zipcode avg_price avg_price_per_sqft avg_sqft_living avg_sqft_lot avg_age total_houses house_age
zipcode 1.000000 -0.097518 0.151576 -0.408197 -0.348230 0.622144 0.024878 NaN
avg_price -0.097518 1.000000 0.865891 0.765753 -0.077480 0.112726 -0.150655 NaN
avg_price_per_sqft 0.151576 0.865891 1.000000 0.397018 -0.214734 0.471106 -0.078179 NaN
avg_sqft_living -0.408197 0.765753 0.397018 1.000000 0.186817 -0.461699 -0.092070 NaN
avg_sqft_lot -0.348230 -0.077480 -0.214734 0.186817 1.000000 -0.364846 -0.323261 NaN
avg_age 0.622144 0.112726 0.471106 -0.461699 -0.364846 1.000000 -0.145524 NaN
total_houses 0.024878 -0.150655 -0.078179 -0.092070 -0.323261 -0.145524 1.000000 NaN
house_age NaN NaN NaN NaN NaN NaN NaN NaN

However there doesn't appear to be any correlation between the average price per square foot and the age of house, which means it's not really relevant to our end analysis

However Zip codes are still a pretty good way of correlating our listings to other data of interest (employment, annual income, education, modes of transportation). We can use another data source to get this information and compare it to our existing data. https://www.uszipcodes.com has information for each zip code in an easy to parse format, so we can just scrape it for each zip code of interest.

This might be interesting: https://www.unitedstateszipcodes.org/98039/ We can scrape information off this for each zip code (only 70 so should be pretty easy) and do some cool stuff like look at preferred transportation, school enrollment or median salary

In [19]:
data["zipcode"].unique()
Out[19]:
array([98027, 98117, 98029, 98065, 98006, 98106, 98011, 98052, 98133,
       98102, 98001, 98092, 98125, 98059, 98199, 98115, 98107, 98024,
       98155, 98072, 98042, 98116, 98034, 98119, 98077, 98045, 98105,
       98007, 98074, 98166, 98008, 98198, 98003, 98014, 98136, 98023,
       98033, 98038, 98103, 98055, 98075, 98058, 98122, 98053, 98118,
       98112, 98004, 98177, 98019, 98144, 98056, 98005, 98168, 98146,
       98028, 98108, 98040, 98148, 98010, 98030, 98178, 98032, 98109,
       98126, 98031, 98070, 98022, 98188, 98002, 98039])
In [20]:
#data scraping

from bs4 import BeautifulSoup
import csv
import pandas as pd
import requests
import re

#needed to avoid 403 when scraping
headers = {
    'Accept': 'text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7',
    'Accept-Encoding': 'gzip, deflate, br, zstd',
    'Accept-Language': 'en-US,en;q=0.9',
    'Cache-Control': 'no-cache',
    'Content-Type': 'application/x-www-form-urlencoded',
    'Cookie': '_pk_id.29.e1c2=968bcc07b503e521.1718492157.; _li_dcdm_c=.unitedstateszipcodes.org; _lc2_fpi=16307b161960--01j0f1tnk55mz01jmc7j0n6f4e; _lc2_fpi_meta=%7B%22w%22%3A1718492157541%7D; cookie=648b908f-3427-4565-9b77-6d7d2cf00ee6; cookie_cst=zix7LPQsHA%3D%3D; _lr_env_src_ats=false; pbjs_fabrickId=%7B%22fabrickId%22%3A%22E1%3ABYenz68hhbaBPFJ1Oj_JfqhZdleyyEAv3MXzzDpE6CReGlkktJA3lH3MDFyhym_EWoRqQxCPIQwjZRGnabsXQNLHY1PUkXC4K3eblBLxttU%22%7D; pbjs_fabrickId_cst=zix7LPQsHA%3D%3D; ccuid=2d625ca7-9c69-4080-9aba-7609f84a642d; _au_1d=AU1D-0100-001718492158-GDMN4A82-A886; __qca=P0-2052112755-1718492157874; _gid=GA1.2.1291931010.1718492158; TAPAD=%7B%22id%22%3A%2240eada16-938c-4448-beaf-90cf62ce46dc%22%7D; _ga_FVWZ0RM4DH=GS1.1.1718554833.3.0.1718554833.60.0.0; _pk_ref.29.e1c2=%5B%22%22%2C%22%22%2C1718554834%2C%22https%3A%2F%2Fwww.google.com%2F%22%5D; _pk_ses.29.e1c2=1; _lr_retry_request=true; cto_bidid=cnESVV9RNkZPRFp3RDglMkJtbHk4bGFuVzZUQndic0l2ckNWciUyRk1iMWhIJTJCbHBoMUdyUDdLJTJGeXY4SW9OOTAxMmh3c2FxMWNUa2pad1lFRmhWc2RmT1Z1RTh4UXU0RDRkZ1Z3bkV0TXVTNGx3MkY4MEpIRktqYVZkaWxodVhUWThDTFRjMlZU; cto_bundle=7ktvOV9MciUyRmd1UGRPYm51bEolMkJIakxuT3VyYlZEdEFQR25WYktXc0s5ZUZxTGIlMkZnQ3llYmRIRTglMkYlMkJKVGpBMTFnMSUyRmdBekk0elp6ellUVzYzUUZzMkRIZnZ0a29GM09xanNrVGgxZnk2R3BqSjZQRSUyRmZ2NUp4d1UlMkJqME81Zzl4RHRyVHpjbThZNWh1RTNCciUyQkp0d2x0cFRnWk51WVkxc1RMemthckpucXBDaUxEUnclM0Q; _ga=GA1.2.1875332805.1718492158; __gads=ID=c3827d46571af6b6:T=1718492159:RT=1718554835:S=ALNI_MbF3JKPcwhXpg35XAKEgxes68-f9A; __gpi=UID=00000e2b1626d22d:T=1718492159:RT=1718554835:S=ALNI_MaaESawrsYVZVFcWJE30dFjsbQ2sg; __eoi=ID=7a68658352ef795b:T=1718492159:RT=1718554835:S=AA-AfjYDklsM5NxCrHNXmNd2hVS4; datadome=J~WQOWI5swjXmp~QZmI5Uf0JqgJNeb5sYpoyJyUEJYQBXs1_pYjlIB8S7jCfSUbJaCVNudVVr5IR1m9ThUYrZVduJ7ec1j7GjLWjz6R~qAwK0~zr2Lz1g0gQWk0RnYCX',
    'Origin': 'https://www.unitedstateszipcodes.org',
    'Pragma': 'no-cache',
    'Priority': 'u=0,i',
    'Referer': "https://www.unitedstateszipcodes.org/",
    'Sec-Ch-Ua': '"Google Chrome";v="125", "Chromium";v="125", "Not.A/Brand";v="24"',
    'Sec-Ch-Ua-Mobile': "?0",
    'Sec-Ch-Ua-Platform': '"Windows"',
    'Sec-Fetch-Dest': 'document',
    'Sec-Fetch-Mode': 'navigate',
    'Sec-Fetch-Site': 'same-origin',
    'Sec-Fetch-User': '?1',
    'Upgrade-Insecure-Requests': '1',
    'User-Agent': "Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/125.0.0.0 Safari/537.36"
}

#much of the data is in tables;
#tags_of_interest contains the labeled data we care about
#when the tuple has two elements the first is the tag and the second is the label
#when the tuple has three elements, the third is the key for the dictionary
tags_of_interest = [("th", "Population"), ("th", "Population Density"), ("th", "Housing Units"), ("th", "Median Home Value"), ("th", "Land Area"), ("th", "Water Area"), ("th", "Occupied Housing Units"), ("th", "Median Household Income"),
                    ("td", "Median Age: ", "Median Age"), ("td", "Male Median Age: ", "Male Median Age"), ("td", "Female Median Age: ", "Female Median Age"), ("th", 'Male', "Male Population"), ("th", "Female", "Female Population"), ("th", "White", "White Population"), ("th", "Black", "Black or African American Population"), ("th", "American Indian", "American Indian or Alaskan Native Population"), ("th", "Asian", "Asian Population"), ("th", "Hawaiian", "Native Hawaiian and Other Pacific Islander Population"), ("th", "Other Race", "Other Race Population"), ("th", "Two Or More Races", "Two or More Races Population"), ("th", "Husband Wife", "Husband and Wife Family Households"), ("th", "Single Guardian", "Single Guardian Households"), ("th", "Singles", "Singles Households"), ("th", "Singles With Roommate", "Singles with Roommate Households"), ("th", "Households without Kids"), ("th", "Households with Kids"), ("th", "In Occupied Housing Units"), ("th", "Correctional Facility", "Correctional Facilities"), ("th", "Juvenile Facilities"), ("th", "Nursing Facilities"), ("th", "Other Institutional"), ("th", "College Student Housing"), ("th", "Military Quarters"), ("th", "Other Noninstitutional"), ("th", "Owned Households With A Mortgage", "Owned House with Mortgage"), ("th", "Owned Households Free", "Owned House Entirely"), ("th", "Renter Occupied Households", "House Occupied by Renter"), ("th", "Households Vacant"), ("th", "Studio Apartment", "Rented Studio Apartment"), ("th", "1 Bedroom", "Rented 1 Bedroom"), ("th", "2 Bedroom", "Rented 2 Bedroom"), ("th", "3+ Bedroom", "Rented 3+ Bedroom"), ("th", "Worked Full-time"), ("th", "Worked Part-time"), ("th", "No Earnings"), ("th", "Car, truck, or van", "Commute in Car, Truck, or Van"), ("th", "Public transportation", "Commute in Public Transportation"), ("th", "Taxicab", "Commute in Taxicab"), ("th", "Motorcycle", "Commute in Motorcycle"), ("th", "Bicycle", "Commute in Bicycle, Walking, Other"), ("th", "Worked at Home"), ("th", "Less than High School Diploma"), ("th", "High School Graduate"), ("th", "Associate's degree"), ("th", "Master's degree"), ("th", "Professional school degree"), ("th", "Doctorate degree"), ("th", "Enrolled in Public School"), ("th", "Enrolled in Private School"), ("th", "Not Enrolled in School")]

#get_sibling_after gets the value of the sibling after the tag with label
def get_sibling_after(soup, tag, label):
    #find_contains returns true if tag.text contains label
    def find_contains(value):
        return value.name == tag and label in value.text.replace('\xa0', '')
    return soup.find(find_contains).find_next_sibling().text



zipcodes = [98027, 98117, 98029, 98065, 98006, 98106, 98011, 98052, 98133,
       98102, 98001, 98092, 98125, 98059, 98199, 98115, 98107, 98024,
       98155, 98072, 98042, 98116, 98034, 98119, 98077, 98045, 98105,
       98007, 98074, 98166, 98008, 98198, 98003, 98014, 98136, 98023,
       98033, 98038, 98103, 98055, 98075, 98058, 98122, 98053, 98118,
       98112, 98004, 98177, 98019, 98144, 98056, 98005, 98168, 98146,
       98028, 98108, 98040, 98148, 98010, 98030, 98178, 98032, 98109,
       98126, 98031, 98070, 98022, 98188, 98002, 98039]

zipcode_data = []
for zipcode in zipcodes:
    url = f"https://www.unitedstateszipcodes.org/{zipcode}/"
    print(f"Now scraping: {zipcode}\nURL: {url}\n")
    page = requests.get(url, headers=headers)
    soup = BeautifulSoup(page.content, "html.parser")
    zdata = {"zipcode": zipcode}
    for tag in tags_of_interest:
        key = tag[2] if len(tag) == 3 else tag[1]
        zdata[key] = get_sibling_after(soup, tag[0], tag[1])
    zipcode_data.append(zdata)


#print(zipcode_data)


scraped_df = pd.DataFrame(zipcode_data).set_index('zipcode')
print(scraped_df.head())
scraped_df.to_csv("zipcode_data.csv")
Now scraping: 98027
URL: https://www.unitedstateszipcodes.org/98027/

Now scraping: 98117
URL: https://www.unitedstateszipcodes.org/98117/

Now scraping: 98029
URL: https://www.unitedstateszipcodes.org/98029/

Now scraping: 98065
URL: https://www.unitedstateszipcodes.org/98065/

Now scraping: 98006
URL: https://www.unitedstateszipcodes.org/98006/

Now scraping: 98106
URL: https://www.unitedstateszipcodes.org/98106/

Now scraping: 98011
URL: https://www.unitedstateszipcodes.org/98011/

Now scraping: 98052
URL: https://www.unitedstateszipcodes.org/98052/

Now scraping: 98133
URL: https://www.unitedstateszipcodes.org/98133/

Now scraping: 98102
URL: https://www.unitedstateszipcodes.org/98102/

Now scraping: 98001
URL: https://www.unitedstateszipcodes.org/98001/

Now scraping: 98092
URL: https://www.unitedstateszipcodes.org/98092/

Now scraping: 98125
URL: https://www.unitedstateszipcodes.org/98125/

Now scraping: 98059
URL: https://www.unitedstateszipcodes.org/98059/

Now scraping: 98199
URL: https://www.unitedstateszipcodes.org/98199/

Now scraping: 98115
URL: https://www.unitedstateszipcodes.org/98115/

Now scraping: 98107
URL: https://www.unitedstateszipcodes.org/98107/

Now scraping: 98024
URL: https://www.unitedstateszipcodes.org/98024/

Now scraping: 98155
URL: https://www.unitedstateszipcodes.org/98155/

Now scraping: 98072
URL: https://www.unitedstateszipcodes.org/98072/

Now scraping: 98042
URL: https://www.unitedstateszipcodes.org/98042/

Now scraping: 98116
URL: https://www.unitedstateszipcodes.org/98116/

Now scraping: 98034
URL: https://www.unitedstateszipcodes.org/98034/

Now scraping: 98119
URL: https://www.unitedstateszipcodes.org/98119/

Now scraping: 98077
URL: https://www.unitedstateszipcodes.org/98077/

Now scraping: 98045
URL: https://www.unitedstateszipcodes.org/98045/

Now scraping: 98105
URL: https://www.unitedstateszipcodes.org/98105/

Now scraping: 98007
URL: https://www.unitedstateszipcodes.org/98007/

Now scraping: 98074
URL: https://www.unitedstateszipcodes.org/98074/

Now scraping: 98166
URL: https://www.unitedstateszipcodes.org/98166/

Now scraping: 98008
URL: https://www.unitedstateszipcodes.org/98008/

Now scraping: 98198
URL: https://www.unitedstateszipcodes.org/98198/

Now scraping: 98003
URL: https://www.unitedstateszipcodes.org/98003/

Now scraping: 98014
URL: https://www.unitedstateszipcodes.org/98014/

Now scraping: 98136
URL: https://www.unitedstateszipcodes.org/98136/

Now scraping: 98023
URL: https://www.unitedstateszipcodes.org/98023/

Now scraping: 98033
URL: https://www.unitedstateszipcodes.org/98033/

Now scraping: 98038
URL: https://www.unitedstateszipcodes.org/98038/

Now scraping: 98103
URL: https://www.unitedstateszipcodes.org/98103/

Now scraping: 98055
URL: https://www.unitedstateszipcodes.org/98055/

Now scraping: 98075
URL: https://www.unitedstateszipcodes.org/98075/

Now scraping: 98058
URL: https://www.unitedstateszipcodes.org/98058/

Now scraping: 98122
URL: https://www.unitedstateszipcodes.org/98122/

Now scraping: 98053
URL: https://www.unitedstateszipcodes.org/98053/

Now scraping: 98118
URL: https://www.unitedstateszipcodes.org/98118/

Now scraping: 98112
URL: https://www.unitedstateszipcodes.org/98112/

Now scraping: 98004
URL: https://www.unitedstateszipcodes.org/98004/

Now scraping: 98177
URL: https://www.unitedstateszipcodes.org/98177/

Now scraping: 98019
URL: https://www.unitedstateszipcodes.org/98019/

Now scraping: 98144
URL: https://www.unitedstateszipcodes.org/98144/

Now scraping: 98056
URL: https://www.unitedstateszipcodes.org/98056/

Now scraping: 98005
URL: https://www.unitedstateszipcodes.org/98005/

Now scraping: 98168
URL: https://www.unitedstateszipcodes.org/98168/

Now scraping: 98146
URL: https://www.unitedstateszipcodes.org/98146/

Now scraping: 98028
URL: https://www.unitedstateszipcodes.org/98028/

Now scraping: 98108
URL: https://www.unitedstateszipcodes.org/98108/

Now scraping: 98040
URL: https://www.unitedstateszipcodes.org/98040/

Now scraping: 98148
URL: https://www.unitedstateszipcodes.org/98148/

Now scraping: 98010
URL: https://www.unitedstateszipcodes.org/98010/

Now scraping: 98030
URL: https://www.unitedstateszipcodes.org/98030/

Now scraping: 98178
URL: https://www.unitedstateszipcodes.org/98178/

Now scraping: 98032
URL: https://www.unitedstateszipcodes.org/98032/

Now scraping: 98109
URL: https://www.unitedstateszipcodes.org/98109/

Now scraping: 98126
URL: https://www.unitedstateszipcodes.org/98126/

Now scraping: 98031
URL: https://www.unitedstateszipcodes.org/98031/

Now scraping: 98070
URL: https://www.unitedstateszipcodes.org/98070/

Now scraping: 98022
URL: https://www.unitedstateszipcodes.org/98022/

Now scraping: 98188
URL: https://www.unitedstateszipcodes.org/98188/

Now scraping: 98002
URL: https://www.unitedstateszipcodes.org/98002/

Now scraping: 98039
URL: https://www.unitedstateszipcodes.org/98039/

        Population Population Density Housing Units Median Home Value  \
zipcode                                                                 
98027       26,141                469        11,248          $478,800   
98117       31,365              7,953        14,213          $463,500   
98029       24,348              2,719        10,222          $446,900   
98065       12,699                171         4,556          $418,900   
98006       36,364              3,402        13,891          $574,000   

        Land Area Water Area Occupied Housing Units Median Household Income  \
zipcode                                                                       
98027       55.79       1.13                 10,454                $100,644   
98117        3.94       0.61                 13,667                 $86,986   
98029        8.95       0.02                  9,656                 $99,974   
98065       74.09       0.87                  4,278                $121,415   
98006       10.69       0.75                 13,288                $110,290   

        Median Age Male Median Age  ... Worked at Home  \
zipcode                             ...                  
98027           41              40  ...            900   
98117           40              39  ...          1,363   
98029           35              34  ...            841   
98065           34              34  ...            451   
98006           42              41  ...          1,368   

        Less than High School Diploma High School Graduate Associate's degree  \
zipcode                                                                         
98027                             703                6,547              1,545   
98117                             646                5,998              1,627   
98029                             400                4,577              1,546   
98065                             234                2,747                655   
98006                             559                6,238              1,955   

        Master's degree Professional school degree Doctorate degree  \
zipcode                                                               
98027             3,365                        684              314   
98117             4,072                      1,290              606   
98029             2,925                        593              690   
98065             1,063                        313               90   
98006             4,184                      1,361            1,137   

        Enrolled in Public School Enrolled in Private School  \
zipcode                                                        
98027                       3,680                        711   
98117                       2,831                      1,458   
98029                       4,359                        965   
98065                       2,397                        908   
98006                       6,315                      1,363   

        Not Enrolled in School  
zipcode                         
98027                      286  
98117                      292  
98029                      556  
98065                      213  
98006                      422  

[5 rows x 60 columns]

Once we've scraped the data we'll save it

In [21]:
#comment out if csv doesn't exist yet
scraped_df = pd.read_csv('zipcode_data.csv')


scraped_zipcode_df = pd.merge(zipcode_df, scraped_df, on = 'zipcode', how='left').reset_index()
scraped_zipcode_df.head()
Out[21]:
index zipcode avg_price avg_price_per_sqft avg_sqft_living avg_sqft_lot avg_age total_houses house_age Population ... Worked at Home Less than High School Diploma High School Graduate Associate's degree Master's degree Professional school degree Doctorate degree Enrolled in Public School Enrolled in Private School Not Enrolled in School
0 0 98001 2.808047e+05 151.387938 1900.856354 14937.450276 33.643646 362 NaN 31,911 ... 579 1,957 12,586 3,015 942 152 72 5,979 470 800
1 1 98002 2.342840e+05 151.174091 1627.743719 7517.633166 46.562814 199 NaN 31,647 ... 361 3,924 13,231 1,922 587 149 20 5,325 243 1,112
2 2 98003 2.941113e+05 157.113414 1928.882143 10603.096429 37.457143 280 NaN 44,151 ... 944 3,570 15,997 3,049 1,212 296 156 6,956 601 1,446
3 3 98004 1.355927e+06 475.435611 2909.022082 13104.220820 42.867508 317 NaN 27,946 ... 1,454 653 5,275 1,384 4,170 1,253 715 2,904 1,385 462
4 4 98005 8.101649e+05 314.929231 2656.803571 19928.785714 44.553571 168 NaN 17,714 ... 524 454 2,954 875 2,368 500 412 2,148 566 185

5 rows × 69 columns

Now we can create maps showing how each of these features from the original dataset and the ones we've scraped vary by zipcode, we do this through the use of folium and geopy. after obtaining the washington zipcodes geojson from OpenDataDE (https://github.com/OpenDataDE/State-zip-code-GeoJSON) we can use folium to plot these values by zipcodes as choropleth maps that we will save as html files

In [22]:
zipcodes_geojson = 'washington_zipcodes.geojson'
gdf = gpd.read_file(zipcodes_geojson)


import folium

gdf.to_csv('gdf.csv')

scraped_zipcode_df['Population'] = scraped_zipcode_df['Population'].str.replace(',', '').astype(int)
for column in scraped_zipcode_df.columns:
    if scraped_zipcode_df[column].dtype != 'object':
        scraped_zipcode_df[column].fillna(scraped_zipcode_df[column].mean(),inplace=True)
scraped_zipcode_df = scraped_zipcode_df.apply(pd.to_numeric, errors='coerce')
scraped_zipcode_df.dropna(axis=1, inplace=True)

html_files = []
for column in scraped_zipcode_df.columns:
    if (column != 'zipcode' and column != 'index'):
        print(column)
        column_map = folium.Map(location=[47.6061, -122.3328], zoom_start=10)
        folium.Choropleth(
            geo_data=gdf,
            name=f'choropleth_{column}',
            data=scraped_zipcode_df,
            columns=['zipcode', column],
            key_on='feature.properties.ZCTA5CE10',
            fill_color='YlOrRd',
            fill_opacity=0.7,
            line_opacity=0.2,
            legend_name=f'{column}'
        ).add_to(column_map)

        file_name = f'choropleth_{column}.html'
        html_files.append(file_name)
        column_map.save(file_name)
        print(f'Saved {file_name}')
        column_map
avg_price
Saved choropleth_avg_price.html
avg_price_per_sqft
Saved choropleth_avg_price_per_sqft.html
avg_sqft_living
Saved choropleth_avg_sqft_living.html
avg_sqft_lot
Saved choropleth_avg_sqft_lot.html
avg_age
Saved choropleth_avg_age.html
total_houses
Saved choropleth_total_houses.html
Population
Saved choropleth_Population.html
Land Area
Saved choropleth_Land Area.html
Water Area
Saved choropleth_Water Area.html
Median Age
Saved choropleth_Median Age.html
Male Median Age
Saved choropleth_Male Median Age.html
Female Median Age
Saved choropleth_Female Median Age.html
Correctional Facilities
Saved choropleth_Correctional Facilities.html
Juvenile Facilities
Saved choropleth_Juvenile Facilities.html
Nursing Facilities
Saved choropleth_Nursing Facilities.html
Other Institutional
Saved choropleth_Other Institutional.html
Military Quarters
Saved choropleth_Military Quarters.html
Other Noninstitutional
Saved choropleth_Other Noninstitutional.html
Commute in Taxicab
Saved choropleth_Commute in Taxicab.html
Commute in Motorcycle
Saved choropleth_Commute in Motorcycle.html

We can display these html files in the colab, however you may have trouble viewing them as a submission, so it may be easier to simply open the saved html file created by this script saved in the folder of this project

In [23]:
from IPython.display import IFrame

for html_file in html_files:
    print(html_file)
    display(IFrame(html_file, width=700, height=500))
choropleth_avg_price.html
choropleth_avg_price_per_sqft.html
choropleth_avg_sqft_living.html
choropleth_avg_sqft_lot.html
choropleth_avg_age.html
choropleth_total_houses.html
choropleth_Population.html
choropleth_Land Area.html
choropleth_Water Area.html
choropleth_Median Age.html
choropleth_Male Median Age.html
choropleth_Female Median Age.html
choropleth_Correctional Facilities.html
choropleth_Juvenile Facilities.html
choropleth_Nursing Facilities.html
choropleth_Other Institutional.html
choropleth_Military Quarters.html
choropleth_Other Noninstitutional.html
choropleth_Commute in Taxicab.html
choropleth_Commute in Motorcycle.html

Using our zipcode dataframe, we will perform ANOVA to see if there is a significant difference between zipcodes on average house price and price per square foot. Later, when we need to prune the dataset for relevant features we'll be able to cross reference this against the correlation table and our scraped data to see which features of zipcodes most affect housing prices and prices per square foot

In [24]:
groups = [group['price'].values for name, group in data.groupby('zipcode')]
f_statistic, p_value = stats.f_oneway(*groups)
print(f"F-statistic: {f_statistic}, p-value: {p_value}")
F-statistic: 214.6322029409192, p-value: 0.0
In [25]:
groups = [group['price_per_sqft_living'].values for name, group in data.groupby('zipcode')]
f_statistic, p_value = stats.f_oneway(*groups)
print(f"F-statistic: {f_statistic}, p-value: {p_value}")
F-statistic: 385.57121676127895, p-value: 0.0

As can be seen the variance between zipcodes is extremely high, we can now perform post hoc testing using tukey's HSD

In [26]:
from statsmodels.stats.multicomp import pairwise_tukeyhsd

data_flat = np.concatenate(groups)
labels = []
for i, group in enumerate(groups):
    labels.extend([f"Group{i+1}"] * len(group))
tukey_results = pairwise_tukeyhsd(data_flat, labels)
print(tukey_results)
/home/mihir/anaconda3/lib/python3.11/site-packages/scipy/integrate/_quadpack_py.py:1233: IntegrationWarning: The integral is probably divergent, or slowly convergent.
  quad_r = quad(f, low, high, args=args, full_output=self.full_output,
    Multiple Comparison of Means - Tukey HSD, FWER=0.05    
===========================================================
 group1  group2  meandiff p-adj    lower     upper   reject
-----------------------------------------------------------
 Group1 Group10   74.5993    0.0   47.4408  101.7578   True
 Group1 Group11   71.6966    0.0   39.8838  103.5094   True
 Group1 Group12   51.6138    0.0   24.2241   79.0035   True
 Group1 Group13   30.4185 0.0018    4.7731   56.0639   True
 Group1 Group14   -2.4681    1.0  -23.5761   18.6398  False
 Group1 Group15  103.8457    0.0   66.2659  141.4255   True
 Group1 Group16  100.1844    0.0   78.1593  122.2094   True
 Group1 Group17   73.7551    0.0   49.4957   98.0146   True
 Group1 Group18  120.6829    0.0   97.2432  144.1227   True
 Group1 Group19    3.7683    1.0  -21.1989   28.7354  False
 Group1  Group2   -0.2138    1.0  -27.1943   26.7666  False
 Group1 Group20    9.6525    1.0  -14.8296   34.1345  False
 Group1 Group21    2.8316    1.0  -28.8863   34.5495  False
 Group1 Group22  191.7745    0.0  169.9892  213.5598   True
 Group1 Group23  114.5643    0.0   93.8343  135.2944   True
 Group1 Group24   22.2683 0.0111    1.8562   42.6804   True
 Group1 Group25  416.6954    0.0  370.5681  462.8228   True
 Group1 Group26  235.9046    0.0   211.621  260.1882   True
 Group1 Group27   12.9605 0.9736   -7.7469   33.6679  False
 Group1 Group28   69.0766    0.0    42.977   95.1761   True
 Group1 Group29  128.9984    0.0  108.4784  149.5184   True
 Group1  Group3    5.7255    1.0  -18.6068   30.0578  False
 Group1 Group30  118.0839    0.0     95.97  140.1978   True
 Group1 Group31   29.0146 0.0022     4.377   53.6521   True
 Group1 Group32   64.1482    0.0   42.0472   86.2492   True
 Group1 Group33   26.8164 0.0005    5.2836   48.3492   True
 Group1 Group34   55.8544    0.0   34.4545   77.2543   True
 Group1 Group35   59.4981    0.0    35.839   83.1572   True
 Group1 Group36  129.9554    0.0   97.5458  162.3651   True
 Group1 Group37   96.1241    0.0   71.6165  120.6317   True
 Group1 Group38  114.2834    0.0   92.5997  135.9671   True
 Group1 Group39  117.2519    0.0   94.4792  140.0247   True
 Group1  Group4  324.0477    0.0  300.5297  347.5657   True
 Group1 Group40   92.8904    0.0    65.866  119.9148   True
 Group1 Group41    4.4263    1.0  -18.4764    27.329  False
 Group1 Group42  271.7846    0.0  237.8956  305.6736   True
 Group1 Group43  218.4531    0.0  198.1185  238.7877   True
 Group1 Group44  253.7664    0.0  227.9515  279.5814   True
 Group1 Group45    79.939    0.0   56.7603  103.1177   True
 Group1 Group46   231.564    0.0  206.8733  256.2548   True
 Group1 Group47   73.0553    0.0   45.4732  100.6375   True
 Group1 Group48  282.0133    0.0  248.6097  315.4168   True
 Group1 Group49  287.2499    0.0  262.6387  311.8612   True
 Group1  Group5  163.5413    0.0  134.9997  192.0829   True
 Group1 Group50  202.7563    0.0  182.2977   223.215   True
 Group1 Group51   197.163    0.0  173.8933  220.4327   True
 Group1 Group52  212.1476    0.0  191.4775  232.8177   True
 Group1 Group53  111.8676    0.0   90.8384  132.8968   True
 Group1 Group54  280.8691    0.0   253.188  308.5501   True
 Group1 Group55  216.1262    0.0  192.0316  240.2208   True
 Group1 Group56  131.0837    0.0  109.0336  153.1339   True
 Group1 Group57  141.4079    0.0  118.5546  164.2613   True
 Group1 Group58  102.5927    0.0   81.4399  123.7455   True
 Group1 Group59  185.8301    0.0  161.0583  210.6019   True
 Group1  Group6  147.7035    0.0  126.5867  168.8204   True
 Group1 Group60  160.8539    0.0   137.816  183.8918   True
 Group1 Group61   74.1035    0.0   49.9625   98.2445   True
 Group1 Group62   34.4441 0.5466   -9.1236   78.0118  False
 Group1 Group63   95.1311    0.0   73.5023  116.7599   True
 Group1 Group64   74.8092    0.0   49.7845   99.8339   True
 Group1 Group65   23.9846  0.073   -0.6266   48.5958  False
 Group1 Group66  141.5308    0.0   116.535  166.5266   True
 Group1 Group67    37.815    0.0   13.0159   62.6141   True
 Group1 Group68   17.6194 0.9958  -13.1303    48.369  False
 Group1 Group69   27.0407 0.0077    2.7084    51.373   True
 Group1  Group7  138.6611    0.0  108.3103  169.0118   True
 Group1 Group70  225.1584    0.0  201.6404  248.6764   True
 Group1  Group8  150.3298    0.0  126.0703  174.5893   True
 Group1  Group9   58.7074    0.0   24.1679   93.2469   True
Group10 Group11   -2.9027    1.0  -38.0196   32.2142  False
Group10 Group12  -22.9855 0.7428  -54.1518    8.1808  False
Group10 Group13  -44.1808    0.0  -73.8259  -14.5357   True
Group10 Group14  -77.0674    0.0 -102.8877  -51.2471   True
Group10 Group15   29.2464 0.7879  -11.1687   69.6615  False
Group10 Group16   25.5851 0.0863   -0.9902   52.1603  False
Group10 Group17   -0.8442    1.0  -29.2988   27.6105  False
Group10 Group18   46.0837    0.0   18.3246   73.8427   True
Group10 Group19   -70.831    0.0  -99.8913  -41.7707   True
Group10  Group2  -74.8131    0.0 -105.6204  -44.0059   True
Group10 Group20  -64.9468    0.0  -93.5915  -36.3022   True
Group10 Group21  -71.7677    0.0 -106.7987  -36.7368   True
Group10 Group22  117.1752    0.0   90.7983  143.5521   True
Group10 Group23    39.965    0.0   14.4527   65.4773   True
Group10 Group24   -52.331    0.0  -77.5856  -27.0764   True
Group10 Group25  342.0961    0.0  293.6309  390.5613   True
Group10 Group26  161.3053    0.0  132.8301  189.7805   True
Group10 Group27  -61.6388    0.0  -87.1327  -36.1449   True
Group10 Group28   -5.5227    1.0  -35.5615   24.5161  False
Group10 Group29   54.3991    0.0   29.0572    79.741   True
Group10  Group3  -68.8738    0.0  -97.3905  -40.3571   True
Group10 Group30   43.4846    0.0   16.8356   70.1335   True
Group10 Group31  -45.5847    0.0  -74.3624  -16.8071   True
Group10 Group32  -10.4511    1.0  -37.0894   16.1872  False
Group10 Group33  -47.7829    0.0  -73.9516  -21.6141   True
Group10 Group34  -18.7449 0.8012  -44.8044    7.3146  False
Group10 Group35  -15.1012  0.999  -43.0457   12.8433  False
Group10 Group36   55.3561    0.0   19.6976   91.0146   True
Group10 Group37   21.5248 0.6961   -7.1416   50.1912  False
Group10 Group38   39.6841    0.0    13.391   65.9772   True
Group10 Group39   42.6526    0.0   15.4544   69.8508   True
Group10  Group4  249.4484    0.0  221.6232  277.2735   True
Group10 Group40   18.2911 0.9909  -12.5547   49.1369  False
Group10 Group41   -70.173    0.0    -97.48   -42.866   True
Group10 Group42  197.1853    0.0  160.1771  234.1935   True
Group10 Group43  143.8538    0.0  118.6618  169.0458   True
Group10 Group44  179.1671    0.0  149.3753   208.959   True
Group10 Group45    5.3397    1.0  -22.1992   32.8787  False
Group10 Group46  156.9647    0.0  128.1416  185.7879   True
Group10 Group47   -1.5439    1.0  -32.8795   29.7916  False
Group10 Group48   207.414    0.0  170.8498  243.9781   True
Group10 Group49  212.6506    0.0  183.8955  241.4057   True
Group10  Group5    88.942    0.0   56.7587  121.1253   True
Group10 Group50   128.157    0.0  102.8648  153.4493   True
Group10 Group51  122.5637    0.0   94.9481  150.1793   True
Group10 Group52  137.5483    0.0  112.0847  163.0119   True
Group10 Group53   37.2683    0.0   11.5123   63.0242   True
Group10 Group54  206.2698    0.0  174.8471  237.6924   True
Group10 Group55  141.5269    0.0  113.2128  169.8411   True
Group10 Group56   56.4844    0.0   29.8883   83.0805   True
Group10 Group57   66.8086    0.0    39.543   94.0743   True
Group10 Group58   27.9934 0.0128    2.1364   53.8504   True
Group10 Group59  111.2308    0.0   82.3382  140.1234   True
Group10  Group6   73.1042    0.0   47.2767   98.9318   True
Group10 Group60   86.2546    0.0   58.8341  113.6752   True
Group10 Group61   -0.4958    1.0  -28.8495   27.8579  False
Group10 Group62  -40.1552  0.265  -86.1909    5.8805  False
Group10 Group63   20.5318 0.5787    -5.716   46.7796  False
Group10 Group64    0.2099    1.0  -28.8998   29.3196  False
Group10 Group65  -50.6147    0.0  -79.3698  -21.8596   True
Group10 Group66   66.9315    0.0   37.8466   96.0164   True
Group10 Group67  -36.7843 0.0003  -65.7004   -7.8682   True
Group10 Group68  -56.9799    0.0  -91.1367  -22.8232   True
Group10 Group69  -47.5586    0.0  -76.0754  -19.0419   True
Group10  Group7   64.0618    0.0   30.2637   97.8599   True
Group10 Group70  150.5591    0.0   122.734  178.3842   True
Group10  Group8   75.7305    0.0   47.2759  104.1851   True
Group10  Group9  -15.8919    1.0  -53.4966   21.7129  False
Group11 Group12  -20.0828 0.9964  -55.3789   15.2133  False
Group11 Group13  -41.2781  0.001  -75.2384   -7.3177   True
Group11 Group14  -74.1647    0.0  -104.843  -43.4863   True
Group11 Group15   32.1491 0.7478  -11.5299   75.8281  False
Group11 Group16   28.4878  0.173   -2.8286   59.8042  False
Group11 Group17    2.0586    1.0  -30.8677   34.9848  False
Group11 Group18   48.9864    0.0   16.6593   81.3134   True
Group11 Group19  -67.9283    0.0 -101.3794  -34.4772   True
Group11  Group2  -71.9104    0.0 -106.8899   -36.931   True
Group11 Group20  -62.0441    0.0  -95.1347  -28.9535   True
Group11 Group21   -68.865    0.0  -107.616   -30.114   True
Group11 Group22  120.0779    0.0   88.9297  151.2262   True
Group11 Group23   42.8677    0.0   12.4482   73.2873   True
Group11 Group24  -49.4283    0.0  -79.6321  -19.2245   True
Group11 Group25  344.9988    0.0  293.7802  396.2175   True
Group11 Group26   164.208    0.0   131.264  197.1521   True
Group11 Group27  -58.7361    0.0  -89.1402  -28.3319   True
Group11 Group28     -2.62    1.0  -36.9245   31.6846  False
Group11 Group29   57.3018    0.0    27.025   87.5786   True
Group11  Group3  -65.9711    0.0  -98.9511  -32.9911   True
Group11 Group30   46.3873    0.0   15.0083   77.7663   True
Group11 Group31   -42.682 0.0002  -75.8878   -9.4762   True
Group11 Group32   -7.5484    1.0  -38.9183   23.8215  False
Group11 Group33  -44.8801    0.0  -75.8523   -13.908   True
Group11 Group34  -15.8422 0.9998  -46.7221   15.0378  False
Group11 Group35  -12.1985    1.0  -44.6849    20.288  False
Group11 Group36   58.2589    0.0   18.9396   97.5781   True
Group11 Group37   24.4275 0.7419    -8.682    57.537  False
Group11 Group38   42.5868    0.0   11.5095   73.6641   True
Group11 Group39   45.5553    0.0   13.7086   77.4021   True
Group11  Group4  252.3511    0.0  219.9673  284.7349   True
Group11 Group40   21.1938 0.9861  -13.8195   56.2072  False
Group11 Group41  -67.2703    0.0    -99.21  -35.3305   True
Group11 Group42   200.088    0.0  159.5407  240.6352   True
Group11 Group43  146.7565    0.0   116.605   176.908   True
Group11 Group44  182.0699    0.0  147.9813  216.1584   True
Group11 Group45    8.2424    1.0  -23.8958   40.3807  False
Group11 Group46  159.8675    0.0  126.6222  193.1127   True
Group11 Group47    1.3588    1.0  -34.0869   36.8044  False
Group11 Group48  210.3167    0.0  170.1743  250.4591   True
Group11 Group49  215.5534    0.0  182.3671  248.7396   True
Group11  Group5   91.8447    0.0   55.6475  128.0419   True
Group11 Group50  131.0597    0.0  100.8245   161.295   True
Group11 Group51  125.4665    0.0   93.2625  157.6704   True
Group11 Group52   140.451    0.0  110.0723  170.8298   True
Group11 Group53    40.171 0.0001    9.5468   70.7952   True
Group11 Group54  209.1725    0.0  173.6499  244.6951   True
Group11 Group55  144.4297    0.0  111.6247  177.2346   True
Group11 Group56   59.3872    0.0   28.0531   90.7212   True
Group11 Group57   69.7114    0.0    37.807  101.6158   True
Group11 Group58   30.8961 0.0455    0.1869   61.6054   True
Group11 Group59  114.1335    0.0    80.828   147.439   True
Group11  Group6    76.007    0.0   45.3225  106.6915   True
Group11 Group60   89.1573    0.0   57.1205  121.1942   True
Group11 Group61    2.4069    1.0  -30.4321    35.246  False
Group11 Group62  -37.2524 0.6575  -86.1785   11.6736  False
Group11 Group63   23.4345 0.6811   -7.6045   54.4736  False
Group11 Group64    3.1126    1.0  -30.3814   36.6066  False
Group11 Group65   -47.712    0.0  -80.8983  -14.5257   True
Group11 Group66   69.8342    0.0   36.3618  103.3067   True
Group11 Group67  -33.8816 0.0386  -67.2074   -0.5557   True
Group11 Group68  -54.0772    0.0  -92.0398  -16.1146   True
Group11 Group69  -44.6559    0.0  -77.6359  -11.6759   True
Group11  Group7   66.9645    0.0   29.3243  104.6047   True
Group11 Group70  153.4618    0.0   121.078  185.8456   True
Group11  Group8   78.6332    0.0    45.707  111.5595   True
Group11  Group9  -12.9892    1.0  -54.0816   28.1033  False
Group12 Group13  -21.1953 0.8285  -51.0524    8.6618  False
Group12 Group14  -54.0819    0.0  -80.1453  -28.0185   True
Group12 Group15   52.2319 0.0002    11.661   92.8028   True
Group12 Group16   48.5706    0.0    21.759   75.3821   True
Group12 Group17   22.1414 0.6172   -6.5341   50.8168  False
Group12 Group18   69.0692    0.0   41.0838   97.0545   True
Group12 Group19  -47.8455    0.0  -77.1221   -18.569   True
Group12  Group2  -51.8276    0.0   -82.839  -20.8163   True
Group12 Group20  -41.9613    0.0  -70.8253  -13.0974   True
Group12 Group21  -48.7822    0.0  -83.9928  -13.5717   True
Group12 Group22  140.1607    0.0  113.5458  166.7757   True
Group12 Group23   62.9505    0.0   37.1922   88.7089   True
Group12 Group24  -29.3455 0.0037  -54.8486   -3.8423   True
Group12 Group25  365.0816    0.0  316.4865  413.6768   True
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Group12 Group39   65.6381    0.0    38.209   93.0672   True
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Group12 Group45   28.3252 0.0366    0.5582   56.0923   True
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Group12 Group53   60.2538    0.0   34.2541   86.2535   True
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Group12 Group55  164.5125    0.0  135.9764  193.0485   True
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Group12 Group58   50.9789    0.0   24.8791   77.0787   True
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Group13  Group4  293.6292    0.0  267.2788  319.9796   True
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Group13 Group44  223.3479    0.0  194.9286  251.7673   True
Group13 Group45   49.5205    0.0   23.4725   75.5685   True
Group13 Group46  201.1455    0.0  173.7433  228.5477   True
Group13 Group47   42.6368    0.0   12.6031   72.6706   True
Group13 Group48  251.5948    0.0    216.14  287.0496   True
Group13 Group49  256.8314    0.0  229.5008   284.162   True
Group13  Group5  133.1228    0.0  102.2056    164.04   True
Group13 Group50  172.3378    0.0  148.6776   195.998   True
Group13 Group51  166.7445    0.0  140.6155  192.8736   True
Group13 Group52  181.7291    0.0  157.8858  205.5724   True
Group13 Group53   81.4491    0.0   57.2938  105.6043   True
Group13 Group54  250.4506    0.0   220.326  280.5751   True
Group13 Group55  185.7077    0.0  158.8414   212.574   True
Group13 Group56  100.6652    0.0   75.6161  125.7143   True
Group13 Group57  110.9894    0.0   85.2305  136.7484   True
Group13 Group58   72.1742    0.0   47.9112   96.4371   True
Group13 Group59  155.4116    0.0  127.9363  182.8868   True
Group13  Group6   117.285    0.0   93.0534  141.5166   True
Group13 Group60  130.4354    0.0  104.5126  156.3582   True
Group13 Group61    43.685    0.0   16.7771   70.5929   True
Group13 Group62    4.0256    1.0   -41.134   49.1852  False
Group13 Group63   64.7126    0.0   40.0336   89.3916   True
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Group14 Group24   24.7364 0.0001    6.1418    43.331   True
Group14 Group25  419.1635    0.0  373.8111  464.5159   True
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Group14 Group39    119.72    0.0    98.561   140.879   True
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Group14 Group41    6.8944    1.0  -14.4044   28.1932  False
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Group14 Group47   75.5235    0.0   49.2578  101.7891   True
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Group14 Group59  188.2982    0.0  165.0013  211.5951   True
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Group14 Group60   163.322    0.0  141.8779  184.7661   True
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Group14 Group62   36.9122 0.2904   -5.8341   79.6586  False
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Group14  Group8  152.7979    0.0  130.0465  175.5494   True
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Group34 Group53   56.0132    0.0   36.4238   75.6025   True
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Group34 Group56   75.2293    0.0   54.5478   95.9108   True
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Group57 Group70   83.7505    0.0   60.1087  107.3922   True
Group57  Group8    8.9219    1.0  -15.4576   33.3013  False
Group57  Group9  -82.7005    0.0 -117.3244  -48.0767   True
Group58 Group59   83.2374    0.0   59.8998   106.575   True
Group58  Group6   45.1108    0.0   25.6963   64.5254   True
Group58 Group60   58.2612    0.0    36.773   79.7495   True
Group58 Group61  -28.4892 0.0004  -51.1561   -5.8223   True
Group58 Group62  -68.1486    0.0 -110.9171  -25.3801   True
Group58 Group63   -7.4616    1.0  -27.4318   12.5086  False
Group58 Group64  -27.7835 0.0022  -51.3894   -4.1777   True
Group58 Group65  -78.6081    0.0 -101.7752   -55.441   True
Group58 Group66   38.9381    0.0   15.3629   62.5134   True
Group58 Group67  -64.7777    0.0  -88.1443  -41.4111   True
Group58 Group68  -84.9733    0.0 -114.5798  -55.3669   True
Group58 Group69   -75.552    0.0  -98.4226  -52.6814   True
Group58  Group7   36.0684 0.0007    6.8764   65.2603   True
Group58 Group70  122.5657    0.0  100.5635  144.5679   True
Group58  Group8   47.7371    0.0    24.944   70.5302   True
Group58  Group9  -43.8853 0.0001  -77.4111  -10.3595   True
Group59  Group6  -38.1266    0.0  -61.4316  -14.8216   True
Group59 Group60  -24.9762 0.0526   -50.035    0.0826  False
Group59 Group61 -111.7266    0.0 -137.8032    -85.65   True
Group59 Group62  -151.386    0.0 -196.0552 -106.7167   True
Group59 Group63   -90.699    0.0 -114.4689  -66.9291   True
Group59 Group64 -111.0209    0.0 -137.9177  -84.1242   True
Group59 Group65 -161.8455    0.0  -188.358  -135.333   True
Group59 Group66  -44.2993    0.0  -71.1692  -17.4294   True
Group59 Group67 -148.0151    0.0 -174.7021 -121.3281   True
Group59 Group68 -168.2107    0.0 -200.5022 -135.9192   True
Group59 Group69 -158.7894    0.0 -185.0432 -132.5356   True
Group59  Group7   -47.169    0.0  -79.0809  -15.2571   True
Group59 Group70   39.3283    0.0   13.8274   64.8292   True
Group59  Group8  -35.5003    0.0  -61.6866    -9.314   True
Group59  Group9 -127.1227    0.0 -163.0417  -91.2036   True
 Group6 Group60   13.1504 0.9822   -8.3025   34.6033  False
 Group6 Group61     -73.6    0.0  -96.2334  -50.9667   True
 Group6 Group62 -113.2594    0.0 -156.0102  -70.5087   True
 Group6 Group63  -52.5724    0.0  -72.5045  -32.6403   True
 Group6 Group64  -72.8944    0.0   -96.468  -49.3207   True
 Group6 Group65 -123.7189    0.0 -146.8532 -100.5847   True
 Group6 Group66   -6.1727    1.0  -29.7157   17.3703  False
 Group6 Group67 -109.8885    0.0 -133.2226  -86.5545   True
 Group6 Group68 -130.0842    0.0  -159.665 -100.5034   True
 Group6 Group69 -120.6629    0.0 -143.5002  -97.8255   True
 Group6  Group7   -9.0425    1.0  -38.2084   20.1234  False
 Group6 Group70   77.4549    0.0   55.4872   99.4225   True
 Group6  Group8    2.6263    1.0  -20.1335    25.386  False
 Group6  Group9  -88.9961    0.0 -122.4992   -55.493   True
Group60 Group61  -86.7504    0.0 -111.1859   -62.315   True
Group60 Group62 -126.4098    0.0 -170.1413  -82.6783   True
Group60 Group63  -65.7228    0.0  -87.6798  -43.7658   True
Group60 Group64  -86.0447    0.0 -111.3536  -60.7359   True
Group60 Group65 -136.8693    0.0 -161.7695 -111.9692   True
Group60 Group66  -19.3231 0.6465  -44.6034    5.9572  False
Group60 Group67 -123.0389    0.0 -148.1248   -97.953   True
Group60 Group68 -143.2345    0.0 -174.2159 -112.2532   True
Group60 Group69 -133.8132    0.0 -158.4377 -109.1888   True
Group60  Group7  -22.1928 0.7818  -52.7783    8.3926  False
Group60 Group70   64.3045    0.0   40.4843   88.1246   True
Group60  Group8  -10.5241    1.0  -35.0766   14.0284  False
Group60  Group9 -102.1465    0.0 -136.8924  -67.4006   True
Group61 Group62  -39.6594 0.2064   -83.982    4.6632  False
Group61 Group63   21.0276 0.1727   -2.0842   44.1394  False
Group61 Group64    0.7057    1.0  -25.6113   27.0227  False
Group61 Group65  -50.1189    0.0   -76.043  -24.1948   True
Group61 Group66   67.4273    0.0   41.1378   93.7168   True
Group61 Group67  -36.2885    0.0  -62.3911  -10.1859   True
Group61 Group68  -56.4841    0.0  -88.2943  -24.6739   True
Group61 Group69  -47.0628    0.0  -72.7223  -21.4033   True
Group61  Group7   64.5576    0.0   33.1328   95.9824   True
Group61 Group70  151.0549    0.0  126.1663  175.9435   True
Group61  Group8   76.2263    0.0   50.6359  101.8167   True
Group61  Group9  -15.3961    1.0   -50.883   20.0909  False
Group62 Group63    60.687    0.0    17.681  103.6929   True
Group62 Group64   40.3651 0.1924    -4.445   85.1751  False
Group62 Group65  -10.4595    1.0    -55.04   34.1209  False
Group62 Group66  107.0867    0.0   62.2928  151.8806   True
Group62 Group67    3.3709    1.0  -41.3136   48.0553  False
Group62 Group68  -16.8248    1.0  -65.0663   31.4168  False
Group62 Group69   -7.4035    1.0  -51.8305   37.0236  False
Group62  Group7   104.217    0.0   56.2287  152.2052   True
Group62 Group70  190.7143    0.0  146.7279  234.7006   True
Group62  Group8  115.8857    0.0   71.4984  160.2729   True
Group62  Group9   24.2633    1.0   -26.478   75.0046  False
Group63 Group64  -20.3219 0.3468  -44.3552    3.7114  False
Group63 Group65  -71.1465    0.0   -94.749   -47.544   True
Group63 Group66   46.3997    0.0   22.3964    70.403   True
Group63 Group67  -57.3161    0.0  -81.1145  -33.5177   True
Group63 Group68  -77.5117    0.0 -107.4601  -47.5633   True
Group63 Group69  -68.0904    0.0   -91.402  -44.7789   True
Group63  Group7     43.53    0.0   13.9913   73.0687   True
Group63 Group70  130.0273    0.0  107.5671  152.4876   True
Group63  Group8   55.1987    0.0   31.9632   78.4342   True
Group63  Group9  -36.4237 0.0142  -70.2518   -2.5955   True
Group64 Group65  -50.8246    0.0  -77.5736  -24.0756   True
Group64 Group66   66.7216    0.0   39.6184   93.8249   True
Group64 Group67  -36.9942    0.0  -63.9161  -10.0722   True
Group64 Group68  -57.1898    0.0  -89.6757  -24.7039   True
Group64 Group69  -47.7685    0.0  -74.2611  -21.2759   True
Group64  Group7   63.8519    0.0   31.7433   95.9605   True
Group64 Group70  150.3492    0.0  124.6026  176.0959   True
Group64  Group8   75.5206    0.0   49.0949  101.9463   True
Group64  Group9  -16.1018    1.0  -52.1957   19.9922  False
Group65 Group66  117.5462    0.0   90.8242  144.2682   True
Group65 Group67   13.8304 0.9996  -12.7077   40.3685  False
Group65 Group68   -6.3652    1.0  -38.5337   25.8033  False
Group65 Group69    3.0561    1.0  -23.0463   29.1585  False
Group65  Group7  114.6765    0.0   82.8891  146.4639   True
Group65 Group70  201.1738    0.0  175.8288  226.5188   True
Group65  Group8  126.3452    0.0  100.3107  152.3797   True
Group65  Group9   34.7228 0.0782   -1.0857   70.5313  False
Group66 Group67 -103.7158    0.0 -130.6109  -76.8207   True
Group66 Group68 -123.9114    0.0 -156.3751  -91.4477   True
Group66 Group69 -114.4901    0.0 -140.9554  -88.0248   True
Group66  Group7   -2.8697    1.0  -34.9558   29.2164  False
Group66 Group70   83.6276    0.0    57.909  109.3462   True
Group66  Group8     8.799    1.0  -17.5994   35.1974  False
Group66  Group9  -82.8234    0.0 -118.8973  -46.7495   True
Group67 Group68  -20.1956 0.9743  -52.5081   12.1169  False
Group67 Group69  -10.7743    1.0   -37.054   15.5053  False
Group67  Group7  100.8461    0.0    68.913  132.7792   True
Group67 Group70  187.3434    0.0  161.8159  212.8709   True
Group67  Group8  112.5148    0.0   86.3026   138.727   True
Group67  Group9   20.8924 0.9941  -15.0455   56.8303  False
Group68 Group69    9.4213    1.0  -22.5343   41.3769  False
Group68  Group7  121.0417    0.0   84.2957  157.7877   True
Group68 Group70   207.539    0.0   176.199  238.8791   True
Group68  Group8  132.7104    0.0  100.8102  164.6106   True
Group68  Group9    41.088 0.0365     0.813   81.3631   True
Group69  Group7  111.6204    0.0   80.0484  143.1924   True
Group69 Group70  198.1177    0.0  173.0435   223.192   True
Group69  Group8  123.2891    0.0   97.5181  149.0601   True
Group69  Group9   31.6667 0.2203   -3.9506   67.2841  False
 Group7 Group70   86.4973    0.0   55.5486  117.4461   True
 Group7  Group8   11.6687    1.0  -19.8472   43.1846  False
 Group7  Group9  -79.9537    0.0  -119.925  -39.9824   True
Group70  Group8  -74.8286    0.0  -99.8322   -49.825   True
Group70  Group9  -166.451    0.0 -201.5171 -131.3849   True
 Group8  Group9  -91.6224    0.0   -127.19  -56.0547   True
-----------------------------------------------------------

As we can see there's significant variance between zipcodes, and having a look at the different heatmaps we can see that there's a variety of correlations between more expensive and less expensive zipcodes and other factors. For example there are the obvious ones such as median household income being correlated directly with avg home price in a zipcode but there are also less obvious ones such as more expensive zipcodes (in terms of price per sqft) having higher median ages.

Avg Price per sqft image.png

Median Age image-2.png

There are many more conclusions we can draw from this analysis, however suffice to say that we can confidently reject the null hypothesis and conclude that zipcodes significantly predict house price as a complex function of various other confounding variables that are also tied to zipcode

Seasonality Analysis¶

Next we can see whether the timing of the listing has any effect on the price, we can hypothesize that as the housing market changes this will affect the number, quality and price of the listings that are put up.

In [27]:
data.insert(2, 'Season', "")
def seasonCalc(x):
  winter = [12, 1, 2]
  spring = [3, 4, 5]
  summer = [6, 7, 8]
  fall = [9, 10, 11]
  month = x.month
  if(month in winter):
    return "Winter"
  if(month in spring):
    return "Spring"
  if(month in summer):
    return "Summer"
  if(month in fall):
    return "Fall"

data['Season'] = data['date'].apply(lambda x: seasonCalc(x))
print(data['Season'].value_counts())
Season
Spring    6520
Summer    6331
Fall      5063
Winter    3699
Name: count, dtype: int64

We will perform a Chi-Square Goodness of Fit Analysis on distribution of House Sales for the various seasons.

We must make sure that all requirements to perform the GoF test are met:

1) As we are looking at number sales in each season we have a single categorical variable.

2) As one house sale doesn't impact another house sale we have independence of observations.

3) The data is mutually exclusive since a house can only be sold in a single season.

4) There are atleast 5 house sales in each season.

  • $H_{0}$: The distribution of house sales across the 4 seasons is not uniformly distributed.

  • $H_{A}$: The distribution of house sales across the 4 seasons is not uniformly distributed.

In [28]:
observed_data = data['Season'].value_counts()
expected_data = pd.Series([len(data['Season'])/4] * 4)
_ , p_val = stats.chisquare(observed_data, expected_data)
print(p_val)
2.004746007881965e-205

As p is less than the alpha value of 0.05, we proceed to reject the Null Hypothesis. This means that the distribution of house sales across the 4 seasons is not uniformly distributed.

However, Looking at the data over time there appears to be uniformity indicating no substantial change in price over time.

Based on this visualization we see that the price data is relatively uniform with the price per square foot being between USD 500 and USD 800. This could potentialy be attributed due to some houses having better location and amenities in turn increasing the valuation.

In [29]:
plt.plot(data['date'], data['price'])
plt.title('Price of Houses over Time')
plt.xlabel('Date')
plt.ylabel('Price ($ Millions of USD)')
Out[29]:
Text(0, 0.5, 'Price ($ Millions of USD)')

This data suggests that most houses are priced between USD 500,000 and USD 1,500,000 with the ocassional outlier of a USD 3,000,000+ house.

ML Analysis¶

Now that we know what columns are relevant to predicting price we can see how an ML model performs using all the data available vs only the columns that we have determined are relevant through testing

In [37]:
#Using complete original data
from sklearn.model_selection import train_test_split
Y = data['price']
X = data.drop(['id', 'date', 'price', 'price_per_sqft_living', 'price_per_sqft_lot'], axis=1)
random_state = 42

#As we can't take date we will instead one hot encode the seasons
X['Summer'] = X['Season'].apply(lambda x: 1 if x == 'Summer' else 0)
X['Fall'] = X['Season'].apply(lambda x: 1 if x == 'Fall' else 0)
X['Winter'] = X['Season'].apply(lambda x: 1 if x == 'Winter' else 0)
X['Spring'] = X['Season'].apply(lambda x: 1 if x == 'Spring' else 0)

X = X.drop(['Season'], axis=1)

X_train, X_test, Y_train, Y_test = train_test_split(X, Y, random_state = random_state, shuffle = True)

print(X_train.columns)
Index(['bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors',
       'waterfront', 'view', 'condition', 'grade', 'sqft_above',
       'sqft_basement', 'yr_built', 'yr_renovated', 'zipcode', 'lat', 'long',
       'sqft_living15', 'sqft_lot15', 'house_age', 'years_since_renovation',
       'num_rooms', 'living percentage', 'Summer', 'Fall', 'Winter', 'Spring'],
      dtype='object')
In [38]:
import torch
import torch.nn as nn
import torch.optim as optim
from sklearn.preprocessing import StandardScaler
import time

device = (
    "cuda"
    if torch.cuda.is_available()
    else "mps"
    if torch.backends.mps.is_available()
    else "cpu"
)

#Converting to numpy arrays
X_train = X_train.values
X_test = X_test.values
Y_train = Y_train.values
Y_test = Y_test.values

#Normalizing features
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

#Converting to PyTorch tensors
X_train = torch.tensor(X_train, dtype=torch.float32).to(device)
X_test = torch.tensor(X_test, dtype=torch.float32).to(device)
Y_train = torch.tensor(Y_train, dtype=torch.float32).view(-1, 1).to(device)
Y_test = torch.tensor(Y_test, dtype=torch.float32).view(-1, 1).to(device)

start_time = time.time()

class HousePricePredictor(nn.Module):
    def __init__(self, input_size):
        super(HousePricePredictor, self).__init__()
        self.fc0 = nn.Linear(input_size, 512)
        self.fc1 = nn.Linear(512, 256)
        self.fc2 = nn.Linear(256, 128)
        self.fc3 = nn.Linear(128, 64)
        self.fc4 = nn.Linear(64, 1)
        
        
    def forward(self, x):
        x = torch.relu(self.fc0(x))
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = torch.relu(self.fc3(x))
        x = self.fc4(x)
        return x

input_size = X_train.shape[1]
model = HousePricePredictor(input_size).to(device)

#training loop
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)
train_losses = []
num_epochs = 10000
for epoch in range(num_epochs):
    model.train()
    optimizer.zero_grad()
    outputs = model(X_train)
    loss = criterion(outputs, Y_train)
    loss.backward()
    optimizer.step()
    train_losses.append(loss.item())
    
    if (epoch+1) % 10 == 0:
        print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')

#Evaluating the model
model.eval()
with torch.no_grad():
    predictions = model(X_test)
    test_loss = criterion(predictions, Y_test)
    print(f'Test Loss: {test_loss.item():.4f}')

end_time = time.time()
training_time = end_time - start_time
print(f"Training time: {training_time:.2f} seconds")

plt.plot(range(num_epochs), train_losses, label='Training Losses')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.title('Training Loss Curve')
plt.legend()
plt.show()
Epoch [10/10000], Loss: 433123917824.0000
Epoch [20/10000], Loss: 433086398464.0000
Epoch [30/10000], Loss: 432900997120.0000
Epoch [40/10000], Loss: 432219324416.0000
Epoch [50/10000], Loss: 430147371008.0000
Epoch [60/10000], Loss: 424738095104.0000
Epoch [70/10000], Loss: 412279668736.0000
Epoch [80/10000], Loss: 386660925440.0000
Epoch [90/10000], Loss: 339749470208.0000
Epoch [100/10000], Loss: 265112322048.0000
Epoch [110/10000], Loss: 169517957120.0000
Epoch [120/10000], Loss: 91106967552.0000
Epoch [130/10000], Loss: 72370700288.0000
Epoch [140/10000], Loss: 65880739840.0000
Epoch [150/10000], Loss: 58765479936.0000
Epoch [160/10000], Loss: 55995146240.0000
Epoch [170/10000], Loss: 53035900928.0000
Epoch [180/10000], Loss: 50626605056.0000
Epoch [190/10000], Loss: 48462565376.0000
Epoch [200/10000], Loss: 46523518976.0000
Epoch [210/10000], Loss: 44782870528.0000
Epoch [220/10000], Loss: 43214204928.0000
Epoch [230/10000], Loss: 41808957440.0000
Epoch [240/10000], Loss: 40553193472.0000
Epoch [250/10000], Loss: 39434149888.0000
Epoch [260/10000], Loss: 38440263680.0000
Epoch [270/10000], Loss: 37560139776.0000
Epoch [280/10000], Loss: 36782993408.0000
Epoch [290/10000], Loss: 36097740800.0000
Epoch [300/10000], Loss: 35494440960.0000
Epoch [310/10000], Loss: 34963111936.0000
Epoch [320/10000], Loss: 34494840832.0000
Epoch [330/10000], Loss: 34081173504.0000
Epoch [340/10000], Loss: 33714993152.0000
Epoch [350/10000], Loss: 33390108672.0000
Epoch [360/10000], Loss: 33100457984.0000
Epoch [370/10000], Loss: 32841717760.0000
Epoch [380/10000], Loss: 32609486848.0000
Epoch [390/10000], Loss: 32400347136.0000
Epoch [400/10000], Loss: 32210941952.0000
Epoch [410/10000], Loss: 32038375424.0000
Epoch [420/10000], Loss: 31880232960.0000
Epoch [430/10000], Loss: 31734411264.0000
Epoch [440/10000], Loss: 31598817280.0000
Epoch [450/10000], Loss: 31471691776.0000
Epoch [460/10000], Loss: 31352326144.0000
Epoch [470/10000], Loss: 31239507968.0000
Epoch [480/10000], Loss: 31132770304.0000
Epoch [490/10000], Loss: 31031689216.0000
Epoch [500/10000], Loss: 30935312384.0000
Epoch [510/10000], Loss: 30842927104.0000
Epoch [520/10000], Loss: 30754158592.0000
Epoch [530/10000], Loss: 30668654592.0000
Epoch [540/10000], Loss: 30586189824.0000
Epoch [550/10000], Loss: 30506569728.0000
Epoch [560/10000], Loss: 30429427712.0000
Epoch [570/10000], Loss: 30354374656.0000
Epoch [580/10000], Loss: 30281342976.0000
Epoch [590/10000], Loss: 30210076672.0000
Epoch [600/10000], Loss: 30140502016.0000
Epoch [610/10000], Loss: 30072526848.0000
Epoch [620/10000], Loss: 30005915648.0000
Epoch [630/10000], Loss: 29940422656.0000
Epoch [640/10000], Loss: 29875814400.0000
Epoch [650/10000], Loss: 29812146176.0000
Epoch [660/10000], Loss: 29749243904.0000
Epoch [670/10000], Loss: 29687371776.0000
Epoch [680/10000], Loss: 29626337280.0000
Epoch [690/10000], Loss: 29566353408.0000
Epoch [700/10000], Loss: 29507135488.0000
Epoch [710/10000], Loss: 29448697856.0000
Epoch [720/10000], Loss: 29391077376.0000
Epoch [730/10000], Loss: 29334106112.0000
Epoch [740/10000], Loss: 29277517824.0000
Epoch [750/10000], Loss: 29221152768.0000
Epoch [760/10000], Loss: 29165289472.0000
Epoch [770/10000], Loss: 29109514240.0000
Epoch [780/10000], Loss: 29053777920.0000
Epoch [790/10000], Loss: 28998371328.0000
Epoch [800/10000], Loss: 28942989312.0000
Epoch [810/10000], Loss: 28887760896.0000
Epoch [820/10000], Loss: 28832759808.0000
Epoch [830/10000], Loss: 28777783296.0000
Epoch [840/10000], Loss: 28723167232.0000
Epoch [850/10000], Loss: 28668645376.0000
Epoch [860/10000], Loss: 28613931008.0000
Epoch [870/10000], Loss: 28559278080.0000
Epoch [880/10000], Loss: 28505344000.0000
Epoch [890/10000], Loss: 28451870720.0000
Epoch [900/10000], Loss: 28398575616.0000
Epoch [910/10000], Loss: 28345452544.0000
Epoch [920/10000], Loss: 28292376576.0000
Epoch [930/10000], Loss: 28239382528.0000
Epoch [940/10000], Loss: 28186478592.0000
Epoch [950/10000], Loss: 28133419008.0000
Epoch [960/10000], Loss: 28080265216.0000
Epoch [970/10000], Loss: 28027324416.0000
Epoch [980/10000], Loss: 27974428672.0000
Epoch [990/10000], Loss: 27921641472.0000
Epoch [1000/10000], Loss: 27868985344.0000
Epoch [1010/10000], Loss: 27816202240.0000
Epoch [1020/10000], Loss: 27763116032.0000
Epoch [1030/10000], Loss: 27709845504.0000
Epoch [1040/10000], Loss: 27656546304.0000
Epoch [1050/10000], Loss: 27603286016.0000
Epoch [1060/10000], Loss: 27550144512.0000
Epoch [1070/10000], Loss: 27496970240.0000
Epoch [1080/10000], Loss: 27443752960.0000
Epoch [1090/10000], Loss: 27390631936.0000
Epoch [1100/10000], Loss: 27337426944.0000
Epoch [1110/10000], Loss: 27284236288.0000
Epoch [1120/10000], Loss: 27231059968.0000
Epoch [1130/10000], Loss: 27177678848.0000
Epoch [1140/10000], Loss: 27124379648.0000
Epoch [1150/10000], Loss: 27070978048.0000
Epoch [1160/10000], Loss: 27017254912.0000
Epoch [1170/10000], Loss: 26963578880.0000
Epoch [1180/10000], Loss: 26909933568.0000
Epoch [1190/10000], Loss: 26856103936.0000
Epoch [1200/10000], Loss: 26801776640.0000
Epoch [1210/10000], Loss: 26746687488.0000
Epoch [1220/10000], Loss: 26690914304.0000
Epoch [1230/10000], Loss: 26634422272.0000
Epoch [1240/10000], Loss: 26577299456.0000
Epoch [1250/10000], Loss: 26519674880.0000
Epoch [1260/10000], Loss: 26461413376.0000
Epoch [1270/10000], Loss: 26402387968.0000
Epoch [1280/10000], Loss: 26343202816.0000
Epoch [1290/10000], Loss: 26283976704.0000
Epoch [1300/10000], Loss: 26224678912.0000
Epoch [1310/10000], Loss: 26165026816.0000
Epoch [1320/10000], Loss: 26105061376.0000
Epoch [1330/10000], Loss: 26044751872.0000
Epoch [1340/10000], Loss: 25984067584.0000
Epoch [1350/10000], Loss: 25923155968.0000
Epoch [1360/10000], Loss: 25861971968.0000
Epoch [1370/10000], Loss: 25800706048.0000
Epoch [1380/10000], Loss: 25739409408.0000
Epoch [1390/10000], Loss: 25677963264.0000
Epoch [1400/10000], Loss: 25616107520.0000
Epoch [1410/10000], Loss: 25553678336.0000
Epoch [1420/10000], Loss: 25489989632.0000
Epoch [1430/10000], Loss: 25425082368.0000
Epoch [1440/10000], Loss: 25358571520.0000
Epoch [1450/10000], Loss: 25290956800.0000
Epoch [1460/10000], Loss: 25222920192.0000
Epoch [1470/10000], Loss: 25153998848.0000
Epoch [1480/10000], Loss: 25082609664.0000
Epoch [1490/10000], Loss: 25013000192.0000
Epoch [1500/10000], Loss: 24942618624.0000
Epoch [1510/10000], Loss: 24871286784.0000
Epoch [1520/10000], Loss: 24799436800.0000
Epoch [1530/10000], Loss: 24727476224.0000
Epoch [1540/10000], Loss: 24655945728.0000
Epoch [1550/10000], Loss: 24584853504.0000
Epoch [1560/10000], Loss: 24513675264.0000
Epoch [1570/10000], Loss: 24443078656.0000
Epoch [1580/10000], Loss: 24372166656.0000
Epoch [1590/10000], Loss: 24300632064.0000
Epoch [1600/10000], Loss: 24229189632.0000
Epoch [1610/10000], Loss: 24157954048.0000
Epoch [1620/10000], Loss: 24086927360.0000
Epoch [1630/10000], Loss: 24016021504.0000
Epoch [1640/10000], Loss: 23945369600.0000
Epoch [1650/10000], Loss: 23874996224.0000
Epoch [1660/10000], Loss: 23804323840.0000
Epoch [1670/10000], Loss: 23733319680.0000
Epoch [1680/10000], Loss: 23662077952.0000
Epoch [1690/10000], Loss: 23591053312.0000
Epoch [1700/10000], Loss: 23520391168.0000
Epoch [1710/10000], Loss: 23449720832.0000
Epoch [1720/10000], Loss: 23378688000.0000
Epoch [1730/10000], Loss: 23307786240.0000
Epoch [1740/10000], Loss: 23236585472.0000
Epoch [1750/10000], Loss: 23164921856.0000
Epoch [1760/10000], Loss: 23093024768.0000
Epoch [1770/10000], Loss: 23020957696.0000
Epoch [1780/10000], Loss: 22949011456.0000
Epoch [1790/10000], Loss: 22876897280.0000
Epoch [1800/10000], Loss: 22804723712.0000
Epoch [1810/10000], Loss: 22732040192.0000
Epoch [1820/10000], Loss: 22659487744.0000
Epoch [1830/10000], Loss: 22585982976.0000
Epoch [1840/10000], Loss: 22510757888.0000
Epoch [1850/10000], Loss: 22435039232.0000
Epoch [1860/10000], Loss: 22358675456.0000
Epoch [1870/10000], Loss: 22282219520.0000
Epoch [1880/10000], Loss: 22205505536.0000
Epoch [1890/10000], Loss: 22127888384.0000
Epoch [1900/10000], Loss: 22049689600.0000
Epoch [1910/10000], Loss: 21971152896.0000
Epoch [1920/10000], Loss: 21891864576.0000
Epoch [1930/10000], Loss: 21811134464.0000
Epoch [1940/10000], Loss: 21728698368.0000
Epoch [1950/10000], Loss: 21643464704.0000
Epoch [1960/10000], Loss: 21555875840.0000
Epoch [1970/10000], Loss: 21466712064.0000
Epoch [1980/10000], Loss: 21376112640.0000
Epoch [1990/10000], Loss: 21283313664.0000
Epoch [2000/10000], Loss: 21188759552.0000
Epoch [2010/10000], Loss: 21092435968.0000
Epoch [2020/10000], Loss: 20994107392.0000
Epoch [2030/10000], Loss: 20893739008.0000
Epoch [2040/10000], Loss: 20791101440.0000
Epoch [2050/10000], Loss: 20684789760.0000
Epoch [2060/10000], Loss: 20574599168.0000
Epoch [2070/10000], Loss: 20461643776.0000
Epoch [2080/10000], Loss: 20345655296.0000
Epoch [2090/10000], Loss: 20226410496.0000
Epoch [2100/10000], Loss: 20103139328.0000
Epoch [2110/10000], Loss: 19976273920.0000
Epoch [2120/10000], Loss: 19846488064.0000
Epoch [2130/10000], Loss: 19714979840.0000
Epoch [2140/10000], Loss: 19581093888.0000
Epoch [2150/10000], Loss: 19445839872.0000
Epoch [2160/10000], Loss: 19308279808.0000
Epoch [2170/10000], Loss: 19166873600.0000
Epoch [2180/10000], Loss: 19021690880.0000
Epoch [2190/10000], Loss: 18875041792.0000
Epoch [2200/10000], Loss: 18729256960.0000
Epoch [2210/10000], Loss: 18582267904.0000
Epoch [2220/10000], Loss: 18433560576.0000
Epoch [2230/10000], Loss: 18285217792.0000
Epoch [2240/10000], Loss: 18136616960.0000
Epoch [2250/10000], Loss: 17987756032.0000
Epoch [2260/10000], Loss: 17837690880.0000
Epoch [2270/10000], Loss: 17686052864.0000
Epoch [2280/10000], Loss: 17531879424.0000
Epoch [2290/10000], Loss: 17375600640.0000
Epoch [2300/10000], Loss: 17217865728.0000
Epoch [2310/10000], Loss: 17059779584.0000
Epoch [2320/10000], Loss: 16901090304.0000
Epoch [2330/10000], Loss: 16740779008.0000
Epoch [2340/10000], Loss: 16580083712.0000
Epoch [2350/10000], Loss: 16419234816.0000
Epoch [2360/10000], Loss: 16257790976.0000
Epoch [2370/10000], Loss: 16095084544.0000
Epoch [2380/10000], Loss: 15931526144.0000
Epoch [2390/10000], Loss: 15768222720.0000
Epoch [2400/10000], Loss: 15605518336.0000
Epoch [2410/10000], Loss: 15442877440.0000
Epoch [2420/10000], Loss: 15281520640.0000
Epoch [2430/10000], Loss: 15119843328.0000
Epoch [2440/10000], Loss: 14958709760.0000
Epoch [2450/10000], Loss: 14797286400.0000
Epoch [2460/10000], Loss: 14634669056.0000
Epoch [2470/10000], Loss: 14471868416.0000
Epoch [2480/10000], Loss: 14308187136.0000
Epoch [2490/10000], Loss: 14144666624.0000
Epoch [2500/10000], Loss: 13980708864.0000
Epoch [2510/10000], Loss: 13817159680.0000
Epoch [2520/10000], Loss: 13653061632.0000
Epoch [2530/10000], Loss: 13486576640.0000
Epoch [2540/10000], Loss: 13314198528.0000
Epoch [2550/10000], Loss: 13138299904.0000
Epoch [2560/10000], Loss: 12950436864.0000
Epoch [2570/10000], Loss: 12764236800.0000
Epoch [2580/10000], Loss: 12587486208.0000
Epoch [2590/10000], Loss: 12414268416.0000
Epoch [2600/10000], Loss: 12243549184.0000
Epoch [2610/10000], Loss: 12074473472.0000
Epoch [2620/10000], Loss: 11907896320.0000
Epoch [2630/10000], Loss: 11745350656.0000
Epoch [2640/10000], Loss: 11585308672.0000
Epoch [2650/10000], Loss: 11430145024.0000
Epoch [2660/10000], Loss: 11278936064.0000
Epoch [2670/10000], Loss: 11132106752.0000
Epoch [2680/10000], Loss: 10987561984.0000
Epoch [2690/10000], Loss: 10846710784.0000
Epoch [2700/10000], Loss: 10709570560.0000
Epoch [2710/10000], Loss: 10574758912.0000
Epoch [2720/10000], Loss: 10441657344.0000
Epoch [2730/10000], Loss: 10310834176.0000
Epoch [2740/10000], Loss: 10183040000.0000
Epoch [2750/10000], Loss: 10059055104.0000
Epoch [2760/10000], Loss: 9938721792.0000
Epoch [2770/10000], Loss: 9820856320.0000
Epoch [2780/10000], Loss: 9706504192.0000
Epoch [2790/10000], Loss: 9594488832.0000
Epoch [2800/10000], Loss: 9485031424.0000
Epoch [2810/10000], Loss: 9378639872.0000
Epoch [2820/10000], Loss: 9272140800.0000
Epoch [2830/10000], Loss: 9166880768.0000
Epoch [2840/10000], Loss: 9062151168.0000
Epoch [2850/10000], Loss: 8959307776.0000
Epoch [2860/10000], Loss: 8858350592.0000
Epoch [2870/10000], Loss: 8756534272.0000
Epoch [2880/10000], Loss: 8661329920.0000
Epoch [2890/10000], Loss: 8564367360.0000
Epoch [2900/10000], Loss: 8468385792.0000
Epoch [2910/10000], Loss: 8377244672.0000
Epoch [2920/10000], Loss: 8287601152.0000
Epoch [2930/10000], Loss: 8199349760.0000
Epoch [2940/10000], Loss: 8114779136.0000
Epoch [2950/10000], Loss: 8028698624.0000
Epoch [2960/10000], Loss: 7945261056.0000
Epoch [2970/10000], Loss: 7865004032.0000
Epoch [2980/10000], Loss: 7784518656.0000
Epoch [2990/10000], Loss: 7706725888.0000
Epoch [3000/10000], Loss: 7637889536.0000
Epoch [3010/10000], Loss: 7555919872.0000
Epoch [3020/10000], Loss: 7483069952.0000
Epoch [3030/10000], Loss: 7414327296.0000
Epoch [3040/10000], Loss: 7343202816.0000
Epoch [3050/10000], Loss: 7274842112.0000
Epoch [3060/10000], Loss: 7205709824.0000
Epoch [3070/10000], Loss: 7142199808.0000
Epoch [3080/10000], Loss: 7076720640.0000
Epoch [3090/10000], Loss: 7012910080.0000
Epoch [3100/10000], Loss: 6948173824.0000
Epoch [3110/10000], Loss: 6885165568.0000
Epoch [3120/10000], Loss: 6825755648.0000
Epoch [3130/10000], Loss: 6762736640.0000
Epoch [3140/10000], Loss: 6704155136.0000
Epoch [3150/10000], Loss: 6645750784.0000
Epoch [3160/10000], Loss: 6586749440.0000
Epoch [3170/10000], Loss: 6532270592.0000
Epoch [3180/10000], Loss: 6475646976.0000
Epoch [3190/10000], Loss: 6422570496.0000
Epoch [3200/10000], Loss: 6363180032.0000
Epoch [3210/10000], Loss: 6311463424.0000
Epoch [3220/10000], Loss: 6259980800.0000
Epoch [3230/10000], Loss: 6207683072.0000
Epoch [3240/10000], Loss: 6156358656.0000
Epoch [3250/10000], Loss: 6104972800.0000
Epoch [3260/10000], Loss: 6066157056.0000
Epoch [3270/10000], Loss: 6009049088.0000
Epoch [3280/10000], Loss: 5961495552.0000
Epoch [3290/10000], Loss: 5915039232.0000
Epoch [3300/10000], Loss: 5866169856.0000
Epoch [3310/10000], Loss: 5824683008.0000
Epoch [3320/10000], Loss: 5817724928.0000
Epoch [3330/10000], Loss: 5741366784.0000
Epoch [3340/10000], Loss: 5691905024.0000
Epoch [3350/10000], Loss: 5646948352.0000
Epoch [3360/10000], Loss: 5613484032.0000
Epoch [3370/10000], Loss: 5572694016.0000
Epoch [3380/10000], Loss: 5531217408.0000
Epoch [3390/10000], Loss: 5489067520.0000
Epoch [3400/10000], Loss: 5450274816.0000
Epoch [3410/10000], Loss: 5413888000.0000
Epoch [3420/10000], Loss: 5378019328.0000
Epoch [3430/10000], Loss: 5348468224.0000
Epoch [3440/10000], Loss: 5337790976.0000
Epoch [3450/10000], Loss: 5279621632.0000
Epoch [3460/10000], Loss: 5238903808.0000
Epoch [3470/10000], Loss: 5206509568.0000
Epoch [3480/10000], Loss: 5177607680.0000
Epoch [3490/10000], Loss: 5147188224.0000
Epoch [3500/10000], Loss: 5117051392.0000
Epoch [3510/10000], Loss: 5095810048.0000
Epoch [3520/10000], Loss: 5059245056.0000
Epoch [3530/10000], Loss: 5024903680.0000
Epoch [3540/10000], Loss: 4995672576.0000
Epoch [3550/10000], Loss: 4965655040.0000
Epoch [3560/10000], Loss: 4932336128.0000
Epoch [3570/10000], Loss: 4910925312.0000
Epoch [3580/10000], Loss: 4873300480.0000
Epoch [3590/10000], Loss: 4845272064.0000
Epoch [3600/10000], Loss: 4815678464.0000
Epoch [3610/10000], Loss: 4785000448.0000
Epoch [3620/10000], Loss: 4762200064.0000
Epoch [3630/10000], Loss: 4739947008.0000
Epoch [3640/10000], Loss: 4725755392.0000
Epoch [3650/10000], Loss: 4678748160.0000
Epoch [3660/10000], Loss: 4651635712.0000
Epoch [3670/10000], Loss: 4631448064.0000
Epoch [3680/10000], Loss: 4606099456.0000
Epoch [3690/10000], Loss: 4586647040.0000
Epoch [3700/10000], Loss: 4559008256.0000
Epoch [3710/10000], Loss: 4532440064.0000
Epoch [3720/10000], Loss: 4504173056.0000
Epoch [3730/10000], Loss: 4478772224.0000
Epoch [3740/10000], Loss: 4490721792.0000
Epoch [3750/10000], Loss: 4441214464.0000
Epoch [3760/10000], Loss: 4415414272.0000
Epoch [3770/10000], Loss: 4388819456.0000
Epoch [3780/10000], Loss: 4371911168.0000
Epoch [3790/10000], Loss: 4343999488.0000
Epoch [3800/10000], Loss: 4341228544.0000
Epoch [3810/10000], Loss: 4310995968.0000
Epoch [3820/10000], Loss: 4284592896.0000
Epoch [3830/10000], Loss: 4260595712.0000
Epoch [3840/10000], Loss: 4253179136.0000
Epoch [3850/10000], Loss: 4264627456.0000
Epoch [3860/10000], Loss: 4204399360.0000
Epoch [3870/10000], Loss: 4187966720.0000
Epoch [3880/10000], Loss: 4167394560.0000
Epoch [3890/10000], Loss: 4144654848.0000
Epoch [3900/10000], Loss: 4139485952.0000
Epoch [3910/10000], Loss: 4110624512.0000
Epoch [3920/10000], Loss: 4090775040.0000
Epoch [3930/10000], Loss: 4073754112.0000
Epoch [3940/10000], Loss: 4064495872.0000
Epoch [3950/10000], Loss: 4046294272.0000
Epoch [3960/10000], Loss: 4024271616.0000
Epoch [3970/10000], Loss: 4007167744.0000
Epoch [3980/10000], Loss: 3992166144.0000
Epoch [3990/10000], Loss: 3982580224.0000
Epoch [4000/10000], Loss: 3960576768.0000
Epoch [4010/10000], Loss: 3951496704.0000
Epoch [4020/10000], Loss: 3928729600.0000
Epoch [4030/10000], Loss: 3911944448.0000
Epoch [4040/10000], Loss: 3898537984.0000
Epoch [4050/10000], Loss: 3877900288.0000
Epoch [4060/10000], Loss: 3867506688.0000
Epoch [4070/10000], Loss: 3854564352.0000
Epoch [4080/10000], Loss: 3833911808.0000
Epoch [4090/10000], Loss: 3827783424.0000
Epoch [4100/10000], Loss: 3806002944.0000
Epoch [4110/10000], Loss: 3815466752.0000
Epoch [4120/10000], Loss: 3791600640.0000
Epoch [4130/10000], Loss: 3769274368.0000
Epoch [4140/10000], Loss: 3754488320.0000
Epoch [4150/10000], Loss: 3745528064.0000
Epoch [4160/10000], Loss: 3730535680.0000
Epoch [4170/10000], Loss: 3724446208.0000
Epoch [4180/10000], Loss: 3711760640.0000
Epoch [4190/10000], Loss: 3693253120.0000
Epoch [4200/10000], Loss: 3677035264.0000
Epoch [4210/10000], Loss: 3682590976.0000
Epoch [4220/10000], Loss: 3652941824.0000
Epoch [4230/10000], Loss: 3643554816.0000
Epoch [4240/10000], Loss: 3627898112.0000
Epoch [4250/10000], Loss: 3633274112.0000
Epoch [4260/10000], Loss: 3608836864.0000
Epoch [4270/10000], Loss: 3591535104.0000
Epoch [4280/10000], Loss: 3583310080.0000
Epoch [4290/10000], Loss: 3578410240.0000
Epoch [4300/10000], Loss: 3558219776.0000
Epoch [4310/10000], Loss: 3562994432.0000
Epoch [4320/10000], Loss: 3536808960.0000
Epoch [4330/10000], Loss: 3526701312.0000
Epoch [4340/10000], Loss: 3521273856.0000
Epoch [4350/10000], Loss: 3505239808.0000
Epoch [4360/10000], Loss: 3503477760.0000
Epoch [4370/10000], Loss: 3485618432.0000
Epoch [4380/10000], Loss: 3470586880.0000
Epoch [4390/10000], Loss: 3465895168.0000
Epoch [4400/10000], Loss: 3461206528.0000
Epoch [4410/10000], Loss: 3447182336.0000
Epoch [4420/10000], Loss: 3433201664.0000
Epoch [4430/10000], Loss: 3429462272.0000
Epoch [4440/10000], Loss: 3413472256.0000
Epoch [4450/10000], Loss: 3400540160.0000
Epoch [4460/10000], Loss: 3393595392.0000
Epoch [4470/10000], Loss: 3382243584.0000
Epoch [4480/10000], Loss: 3395930112.0000
Epoch [4490/10000], Loss: 3368309248.0000
Epoch [4500/10000], Loss: 3352822784.0000
Epoch [4510/10000], Loss: 3347123712.0000
Epoch [4520/10000], Loss: 3330389504.0000
Epoch [4530/10000], Loss: 3332773376.0000
Epoch [4540/10000], Loss: 3321235456.0000
Epoch [4550/10000], Loss: 3303904768.0000
Epoch [4560/10000], Loss: 3306193152.0000
Epoch [4570/10000], Loss: 3290996992.0000
Epoch [4580/10000], Loss: 3280463104.0000
Epoch [4590/10000], Loss: 3271142400.0000
Epoch [4600/10000], Loss: 3265650944.0000
Epoch [4610/10000], Loss: 3248799232.0000
Epoch [4620/10000], Loss: 3279291136.0000
Epoch [4630/10000], Loss: 3248885760.0000
Epoch [4640/10000], Loss: 3234096384.0000
Epoch [4650/10000], Loss: 3219590400.0000
Epoch [4660/10000], Loss: 3209147904.0000
Epoch [4670/10000], Loss: 3210303232.0000
Epoch [4680/10000], Loss: 3196377600.0000
Epoch [4690/10000], Loss: 3187228672.0000
Epoch [4700/10000], Loss: 3177142528.0000
Epoch [4710/10000], Loss: 3169658368.0000
Epoch [4720/10000], Loss: 3170015744.0000
Epoch [4730/10000], Loss: 3152867072.0000
Epoch [4740/10000], Loss: 3152425216.0000
Epoch [4750/10000], Loss: 3145518848.0000
Epoch [4760/10000], Loss: 3138225152.0000
Epoch [4770/10000], Loss: 3125236480.0000
Epoch [4780/10000], Loss: 3131133440.0000
Epoch [4790/10000], Loss: 3133558016.0000
Epoch [4800/10000], Loss: 3114557696.0000
Epoch [4810/10000], Loss: 3098081280.0000
Epoch [4820/10000], Loss: 3095632128.0000
Epoch [4830/10000], Loss: 3086028800.0000
Epoch [4840/10000], Loss: 3077510144.0000
Epoch [4850/10000], Loss: 3073416192.0000
Epoch [4860/10000], Loss: 3069588736.0000
Epoch [4870/10000], Loss: 3061447424.0000
Epoch [4880/10000], Loss: 3055464704.0000
Epoch [4890/10000], Loss: 3051583232.0000
Epoch [4900/10000], Loss: 3042648320.0000
Epoch [4910/10000], Loss: 3030856960.0000
Epoch [4920/10000], Loss: 3037825792.0000
Epoch [4930/10000], Loss: 3029419008.0000
Epoch [4940/10000], Loss: 3008811776.0000
Epoch [4950/10000], Loss: 3006854400.0000
Epoch [4960/10000], Loss: 3003416832.0000
Epoch [4970/10000], Loss: 2992418816.0000
Epoch [4980/10000], Loss: 2995773696.0000
Epoch [4990/10000], Loss: 2991357440.0000
Epoch [5000/10000], Loss: 2969836288.0000
Epoch [5010/10000], Loss: 2980129280.0000
Epoch [5020/10000], Loss: 2960833024.0000
Epoch [5030/10000], Loss: 2952809728.0000
Epoch [5040/10000], Loss: 2957916672.0000
Epoch [5050/10000], Loss: 2940487936.0000
Epoch [5060/10000], Loss: 2940962304.0000
Epoch [5070/10000], Loss: 2934764800.0000
Epoch [5080/10000], Loss: 2928993536.0000
Epoch [5090/10000], Loss: 2931434240.0000
Epoch [5100/10000], Loss: 2919537408.0000
Epoch [5110/10000], Loss: 2906075648.0000
Epoch [5120/10000], Loss: 2927224064.0000
Epoch [5130/10000], Loss: 2902827520.0000
Epoch [5140/10000], Loss: 2896520704.0000
Epoch [5150/10000], Loss: 2883586816.0000
Epoch [5160/10000], Loss: 2886972160.0000
Epoch [5170/10000], Loss: 2867039232.0000
Epoch [5180/10000], Loss: 2873439488.0000
Epoch [5190/10000], Loss: 2861988864.0000
Epoch [5200/10000], Loss: 2852918528.0000
Epoch [5210/10000], Loss: 2860087552.0000
Epoch [5220/10000], Loss: 2839692800.0000
Epoch [5230/10000], Loss: 2847145984.0000
Epoch [5240/10000], Loss: 2838629632.0000
Epoch [5250/10000], Loss: 2828067072.0000
Epoch [5260/10000], Loss: 2832134400.0000
Epoch [5270/10000], Loss: 2820568832.0000
Epoch [5280/10000], Loss: 2813483264.0000
Epoch [5290/10000], Loss: 2801124352.0000
Epoch [5300/10000], Loss: 2809410560.0000
Epoch [5310/10000], Loss: 2799358208.0000
Epoch [5320/10000], Loss: 2783502336.0000
Epoch [5330/10000], Loss: 2789405952.0000
Epoch [5340/10000], Loss: 2781915136.0000
Epoch [5350/10000], Loss: 2788878848.0000
Epoch [5360/10000], Loss: 2764881664.0000
Epoch [5370/10000], Loss: 2756023296.0000
Epoch [5380/10000], Loss: 2753573376.0000
Epoch [5390/10000], Loss: 2752476160.0000
Epoch [5400/10000], Loss: 2740486656.0000
Epoch [5410/10000], Loss: 2750493952.0000
Epoch [5420/10000], Loss: 2733755392.0000
Epoch [5430/10000], Loss: 2737707776.0000
Epoch [5440/10000], Loss: 2747668992.0000
Epoch [5450/10000], Loss: 2731519232.0000
Epoch [5460/10000], Loss: 2711805952.0000
Epoch [5470/10000], Loss: 2714754048.0000
Epoch [5480/10000], Loss: 2704708352.0000
Epoch [5490/10000], Loss: 2696717056.0000
Epoch [5500/10000], Loss: 2712837632.0000
Epoch [5510/10000], Loss: 2688124416.0000
Epoch [5520/10000], Loss: 2685782272.0000
Epoch [5530/10000], Loss: 2687791360.0000
Epoch [5540/10000], Loss: 2673448704.0000
Epoch [5550/10000], Loss: 2681891072.0000
Epoch [5560/10000], Loss: 2665351424.0000
Epoch [5570/10000], Loss: 2670198528.0000
Epoch [5580/10000], Loss: 2658390528.0000
Epoch [5590/10000], Loss: 2659404032.0000
Epoch [5600/10000], Loss: 2657780480.0000
Epoch [5610/10000], Loss: 2646512896.0000
Epoch [5620/10000], Loss: 2659298816.0000
Epoch [5630/10000], Loss: 2638614784.0000
Epoch [5640/10000], Loss: 2633453056.0000
Epoch [5650/10000], Loss: 2630362368.0000
Epoch [5660/10000], Loss: 2630851840.0000
Epoch [5670/10000], Loss: 2618382080.0000
Epoch [5680/10000], Loss: 2624424192.0000
Epoch [5690/10000], Loss: 2606528512.0000
Epoch [5700/10000], Loss: 2617516288.0000
Epoch [5710/10000], Loss: 2610330368.0000
Epoch [5720/10000], Loss: 2595715584.0000
Epoch [5730/10000], Loss: 2593130240.0000
Epoch [5740/10000], Loss: 2596262400.0000
Epoch [5750/10000], Loss: 2583693056.0000
Epoch [5760/10000], Loss: 2584419072.0000
Epoch [5770/10000], Loss: 2575296256.0000
Epoch [5780/10000], Loss: 2578001408.0000
Epoch [5790/10000], Loss: 2568302848.0000
Epoch [5800/10000], Loss: 2565744896.0000
Epoch [5810/10000], Loss: 2559791104.0000
Epoch [5820/10000], Loss: 2560289024.0000
Epoch [5830/10000], Loss: 2546059008.0000
Epoch [5840/10000], Loss: 2557901824.0000
Epoch [5850/10000], Loss: 2541013248.0000
Epoch [5860/10000], Loss: 2544367872.0000
Epoch [5870/10000], Loss: 2552157184.0000
Epoch [5880/10000], Loss: 2541111552.0000
Epoch [5890/10000], Loss: 2525993984.0000
Epoch [5900/10000], Loss: 2526525952.0000
Epoch [5910/10000], Loss: 2514047488.0000
Epoch [5920/10000], Loss: 2531786752.0000
Epoch [5930/10000], Loss: 2507421440.0000
Epoch [5940/10000], Loss: 2506919936.0000
Epoch [5950/10000], Loss: 2505056000.0000
Epoch [5960/10000], Loss: 2496488448.0000
Epoch [5970/10000], Loss: 2500248576.0000
Epoch [5980/10000], Loss: 2528514048.0000
Epoch [5990/10000], Loss: 2496539904.0000
Epoch [6000/10000], Loss: 2490183680.0000
Epoch [6010/10000], Loss: 2480079616.0000
Epoch [6020/10000], Loss: 2475218944.0000
Epoch [6030/10000], Loss: 2477799424.0000
Epoch [6040/10000], Loss: 2471250432.0000
Epoch [6050/10000], Loss: 2462772736.0000
Epoch [6060/10000], Loss: 2462651648.0000
Epoch [6070/10000], Loss: 2462771712.0000
Epoch [6080/10000], Loss: 2461954560.0000
Epoch [6090/10000], Loss: 2448605440.0000
Epoch [6100/10000], Loss: 2453399552.0000
Epoch [6110/10000], Loss: 2445027328.0000
Epoch [6120/10000], Loss: 2474389504.0000
Epoch [6130/10000], Loss: 2447848448.0000
Epoch [6140/10000], Loss: 2435211008.0000
Epoch [6150/10000], Loss: 2435099136.0000
Epoch [6160/10000], Loss: 2421842176.0000
Epoch [6170/10000], Loss: 2424975104.0000
Epoch [6180/10000], Loss: 2419620608.0000
Epoch [6190/10000], Loss: 2418585856.0000
Epoch [6200/10000], Loss: 2413898752.0000
Epoch [6210/10000], Loss: 2411735040.0000
Epoch [6220/10000], Loss: 2413238784.0000
Epoch [6230/10000], Loss: 2400744960.0000
Epoch [6240/10000], Loss: 2411193856.0000
Epoch [6250/10000], Loss: 2388815104.0000
Epoch [6260/10000], Loss: 2398650880.0000
Epoch [6270/10000], Loss: 2387508224.0000
Epoch [6280/10000], Loss: 2393847296.0000
Epoch [6290/10000], Loss: 2381820672.0000
Epoch [6300/10000], Loss: 2387097856.0000
Epoch [6310/10000], Loss: 2378995968.0000
Epoch [6320/10000], Loss: 2374241024.0000
Epoch [6330/10000], Loss: 2363242496.0000
Epoch [6340/10000], Loss: 2386127360.0000
Epoch [6350/10000], Loss: 2365661696.0000
Epoch [6360/10000], Loss: 2353520640.0000
Epoch [6370/10000], Loss: 2358082048.0000
Epoch [6380/10000], Loss: 2346872576.0000
Epoch [6390/10000], Loss: 2360679168.0000
Epoch [6400/10000], Loss: 2341180160.0000
Epoch [6410/10000], Loss: 2388291072.0000
Epoch [6420/10000], Loss: 2346024704.0000
Epoch [6430/10000], Loss: 2347440384.0000
Epoch [6440/10000], Loss: 2327400960.0000
Epoch [6450/10000], Loss: 2329484032.0000
Epoch [6460/10000], Loss: 2323392768.0000
Epoch [6470/10000], Loss: 2322240000.0000
Epoch [6480/10000], Loss: 2323016960.0000
Epoch [6490/10000], Loss: 2321670400.0000
Epoch [6500/10000], Loss: 2310045952.0000
Epoch [6510/10000], Loss: 2316552960.0000
Epoch [6520/10000], Loss: 2304182784.0000
Epoch [6530/10000], Loss: 2310857472.0000
Epoch [6540/10000], Loss: 2301212672.0000
Epoch [6550/10000], Loss: 2308807424.0000
Epoch [6560/10000], Loss: 2292982528.0000
Epoch [6570/10000], Loss: 2311119360.0000
Epoch [6580/10000], Loss: 2294327296.0000
Epoch [6590/10000], Loss: 2294208256.0000
Epoch [6600/10000], Loss: 2282809344.0000
Epoch [6610/10000], Loss: 2282838528.0000
Epoch [6620/10000], Loss: 2277477888.0000
Epoch [6630/10000], Loss: 2299635200.0000
Epoch [6640/10000], Loss: 2283662080.0000
Epoch [6650/10000], Loss: 2271457792.0000
Epoch [6660/10000], Loss: 2262554368.0000
Epoch [6670/10000], Loss: 2281238528.0000
Epoch [6680/10000], Loss: 2260258560.0000
Epoch [6690/10000], Loss: 2261393920.0000
Epoch [6700/10000], Loss: 2260733696.0000
Epoch [6710/10000], Loss: 2249516800.0000
Epoch [6720/10000], Loss: 2272617216.0000
Epoch [6730/10000], Loss: 2250735360.0000
Epoch [6740/10000], Loss: 2240633344.0000
Epoch [6750/10000], Loss: 2248001024.0000
Epoch [6760/10000], Loss: 2246560000.0000
Epoch [6770/10000], Loss: 2253022976.0000
Epoch [6780/10000], Loss: 2236257280.0000
Epoch [6790/10000], Loss: 2229622528.0000
Epoch [6800/10000], Loss: 2228794112.0000
Epoch [6810/10000], Loss: 2225636352.0000
Epoch [6820/10000], Loss: 2238477568.0000
Epoch [6830/10000], Loss: 2215875072.0000
Epoch [6840/10000], Loss: 2230727936.0000
Epoch [6850/10000], Loss: 2213054720.0000
Epoch [6860/10000], Loss: 2221588992.0000
Epoch [6870/10000], Loss: 2205377024.0000
Epoch [6880/10000], Loss: 2213481728.0000
Epoch [6890/10000], Loss: 2215842816.0000
Epoch [6900/10000], Loss: 2204030208.0000
Epoch [6910/10000], Loss: 2242064384.0000
Epoch [6920/10000], Loss: 2202931456.0000
Epoch [6930/10000], Loss: 2191331328.0000
Epoch [6940/10000], Loss: 2199475968.0000
Epoch [6950/10000], Loss: 2185612288.0000
Epoch [6960/10000], Loss: 2193490176.0000
Epoch [6970/10000], Loss: 2188136448.0000
Epoch [6980/10000], Loss: 2180539392.0000
Epoch [6990/10000], Loss: 2194154752.0000
Epoch [7000/10000], Loss: 2181321984.0000
Epoch [7010/10000], Loss: 2174782464.0000
Epoch [7020/10000], Loss: 2181085184.0000
Epoch [7030/10000], Loss: 2168049152.0000
Epoch [7040/10000], Loss: 2187429632.0000
Epoch [7050/10000], Loss: 2182571264.0000
Epoch [7060/10000], Loss: 2163437568.0000
Epoch [7070/10000], Loss: 2169222912.0000
Epoch [7080/10000], Loss: 2155181824.0000
Epoch [7090/10000], Loss: 2166765056.0000
Epoch [7100/10000], Loss: 2149235456.0000
Epoch [7110/10000], Loss: 2160807424.0000
Epoch [7120/10000], Loss: 2148117248.0000
Epoch [7130/10000], Loss: 2166810368.0000
Epoch [7140/10000], Loss: 2161579776.0000
Epoch [7150/10000], Loss: 2143908352.0000
Epoch [7160/10000], Loss: 2137140864.0000
Epoch [7170/10000], Loss: 2169488640.0000
Epoch [7180/10000], Loss: 2134905344.0000
Epoch [7190/10000], Loss: 2129259520.0000
Epoch [7200/10000], Loss: 2132582784.0000
Epoch [7210/10000], Loss: 2130287360.0000
Epoch [7220/10000], Loss: 2133077504.0000
Epoch [7230/10000], Loss: 2128887680.0000
Epoch [7240/10000], Loss: 2118246784.0000
Epoch [7250/10000], Loss: 2124708096.0000
Epoch [7260/10000], Loss: 2116986624.0000
Epoch [7270/10000], Loss: 2142621824.0000
Epoch [7280/10000], Loss: 2112934144.0000
Epoch [7290/10000], Loss: 2108426496.0000
Epoch [7300/10000], Loss: 2141994112.0000
Epoch [7310/10000], Loss: 2111977088.0000
Epoch [7320/10000], Loss: 2099641216.0000
Epoch [7330/10000], Loss: 2101525504.0000
Epoch [7340/10000], Loss: 2101151360.0000
Epoch [7350/10000], Loss: 2094671872.0000
Epoch [7360/10000], Loss: 2105047296.0000
Epoch [7370/10000], Loss: 2089033472.0000
Epoch [7380/10000], Loss: 2097452800.0000
Epoch [7390/10000], Loss: 2092215424.0000
Epoch [7400/10000], Loss: 2124631168.0000
Epoch [7410/10000], Loss: 2095457152.0000
Epoch [7420/10000], Loss: 2086641664.0000
Epoch [7430/10000], Loss: 2077890688.0000
Epoch [7440/10000], Loss: 2073734272.0000
Epoch [7450/10000], Loss: 2092171520.0000
Epoch [7460/10000], Loss: 2074749952.0000
Epoch [7470/10000], Loss: 2066467968.0000
Epoch [7480/10000], Loss: 2072594816.0000
Epoch [7490/10000], Loss: 2066668032.0000
Epoch [7500/10000], Loss: 2093650432.0000
Epoch [7510/10000], Loss: 2070081280.0000
Epoch [7520/10000], Loss: 2060846080.0000
Epoch [7530/10000], Loss: 2055336064.0000
Epoch [7540/10000], Loss: 2057551872.0000
Epoch [7550/10000], Loss: 2063753472.0000
Epoch [7560/10000], Loss: 2054878464.0000
Epoch [7570/10000], Loss: 2057580416.0000
Epoch [7580/10000], Loss: 2050848128.0000
Epoch [7590/10000], Loss: 2054713344.0000
Epoch [7600/10000], Loss: 2038613248.0000
Epoch [7610/10000], Loss: 2050299392.0000
Epoch [7620/10000], Loss: 2037352576.0000
Epoch [7630/10000], Loss: 2076525824.0000
Epoch [7640/10000], Loss: 2048320256.0000
Epoch [7650/10000], Loss: 2033467776.0000
Epoch [7660/10000], Loss: 2029393152.0000
Epoch [7670/10000], Loss: 2056397696.0000
Epoch [7680/10000], Loss: 2022746368.0000
Epoch [7690/10000], Loss: 2027116160.0000
Epoch [7700/10000], Loss: 2025189888.0000
Epoch [7710/10000], Loss: 2019562880.0000
Epoch [7720/10000], Loss: 2020281984.0000
Epoch [7730/10000], Loss: 2038843520.0000
Epoch [7740/10000], Loss: 2033569280.0000
Epoch [7750/10000], Loss: 2012242176.0000
Epoch [7760/10000], Loss: 2012098560.0000
Epoch [7770/10000], Loss: 2009663872.0000
Epoch [7780/10000], Loss: 2014582016.0000
Epoch [7790/10000], Loss: 2014556160.0000
Epoch [7800/10000], Loss: 2032128640.0000
Epoch [7810/10000], Loss: 2011707776.0000
Epoch [7820/10000], Loss: 2002769408.0000
Epoch [7830/10000], Loss: 1997468288.0000
Epoch [7840/10000], Loss: 2001800064.0000
Epoch [7850/10000], Loss: 1992898048.0000
Epoch [7860/10000], Loss: 2003023744.0000
Epoch [7870/10000], Loss: 1991664384.0000
Epoch [7880/10000], Loss: 1995576960.0000
Epoch [7890/10000], Loss: 1989745920.0000
Epoch [7900/10000], Loss: 1990721792.0000
Epoch [7910/10000], Loss: 1992482176.0000
Epoch [7920/10000], Loss: 1988452224.0000
Epoch [7930/10000], Loss: 1990443136.0000
Epoch [7940/10000], Loss: 1972082560.0000
Epoch [7950/10000], Loss: 1981559552.0000
Epoch [7960/10000], Loss: 1973150464.0000
Epoch [7970/10000], Loss: 1999383296.0000
Epoch [7980/10000], Loss: 1967027200.0000
Epoch [7990/10000], Loss: 1981695488.0000
Epoch [8000/10000], Loss: 1965170688.0000
Epoch [8010/10000], Loss: 1974881536.0000
Epoch [8020/10000], Loss: 1961249408.0000
Epoch [8030/10000], Loss: 1965836032.0000
Epoch [8040/10000], Loss: 1961008000.0000
Epoch [8050/10000], Loss: 1962919680.0000
Epoch [8060/10000], Loss: 1956431616.0000
Epoch [8070/10000], Loss: 1959559168.0000
Epoch [8080/10000], Loss: 1965271808.0000
Epoch [8090/10000], Loss: 1966480384.0000
Epoch [8100/10000], Loss: 1952707200.0000
Epoch [8110/10000], Loss: 1942926208.0000
Epoch [8120/10000], Loss: 1958801024.0000
Epoch [8130/10000], Loss: 1947213184.0000
Epoch [8140/10000], Loss: 1946152064.0000
Epoch [8150/10000], Loss: 1947266816.0000
Epoch [8160/10000], Loss: 1932903552.0000
Epoch [8170/10000], Loss: 1947252352.0000
Epoch [8180/10000], Loss: 1948906496.0000
Epoch [8190/10000], Loss: 1935009408.0000
Epoch [8200/10000], Loss: 1928837888.0000
Epoch [8210/10000], Loss: 1926797824.0000
Epoch [8220/10000], Loss: 1933050880.0000
Epoch [8230/10000], Loss: 1941895680.0000
Epoch [8240/10000], Loss: 1933791616.0000
Epoch [8250/10000], Loss: 1924434304.0000
Epoch [8260/10000], Loss: 1918769664.0000
Epoch [8270/10000], Loss: 1921701632.0000
Epoch [8280/10000], Loss: 1919624320.0000
Epoch [8290/10000], Loss: 1936179712.0000
Epoch [8300/10000], Loss: 1915673728.0000
Epoch [8310/10000], Loss: 1911277824.0000
Epoch [8320/10000], Loss: 1925158912.0000
Epoch [8330/10000], Loss: 1907324032.0000
Epoch [8340/10000], Loss: 1911923328.0000
Epoch [8350/10000], Loss: 1910498048.0000
Epoch [8360/10000], Loss: 1926257408.0000
Epoch [8370/10000], Loss: 1899247744.0000
Epoch [8380/10000], Loss: 1907998720.0000
Epoch [8390/10000], Loss: 1896338432.0000
Epoch [8400/10000], Loss: 1906887424.0000
Epoch [8410/10000], Loss: 1891608192.0000
Epoch [8420/10000], Loss: 1920566400.0000
Epoch [8430/10000], Loss: 1911195904.0000
Epoch [8440/10000], Loss: 1886211712.0000
Epoch [8450/10000], Loss: 1890839296.0000
Epoch [8460/10000], Loss: 1888867072.0000
Epoch [8470/10000], Loss: 1898294400.0000
Epoch [8480/10000], Loss: 1902750848.0000
Epoch [8490/10000], Loss: 1881236096.0000
Epoch [8500/10000], Loss: 1879642880.0000
Epoch [8510/10000], Loss: 1878988032.0000
Epoch [8520/10000], Loss: 1884136192.0000
Epoch [8530/10000], Loss: 1920661888.0000
Epoch [8540/10000], Loss: 1879233408.0000
Epoch [8550/10000], Loss: 1873678592.0000
Epoch [8560/10000], Loss: 1867909376.0000
Epoch [8570/10000], Loss: 1869823232.0000
Epoch [8580/10000], Loss: 1864174080.0000
Epoch [8590/10000], Loss: 1873981568.0000
Epoch [8600/10000], Loss: 1864399104.0000
Epoch [8610/10000], Loss: 1888421888.0000
Epoch [8620/10000], Loss: 1868284416.0000
Epoch [8630/10000], Loss: 1856559232.0000
Epoch [8640/10000], Loss: 1865983360.0000
Epoch [8650/10000], Loss: 1857273856.0000
Epoch [8660/10000], Loss: 1870807168.0000
Epoch [8670/10000], Loss: 1851502592.0000
Epoch [8680/10000], Loss: 1864405760.0000
Epoch [8690/10000], Loss: 1861639296.0000
Epoch [8700/10000], Loss: 1855030144.0000
Epoch [8710/10000], Loss: 1855192832.0000
Epoch [8720/10000], Loss: 1844568320.0000
Epoch [8730/10000], Loss: 1847132160.0000
Epoch [8740/10000], Loss: 1851677568.0000
Epoch [8750/10000], Loss: 1853071616.0000
Epoch [8760/10000], Loss: 1847882624.0000
Epoch [8770/10000], Loss: 1848881152.0000
Epoch [8780/10000], Loss: 1834388480.0000
Epoch [8790/10000], Loss: 1850166400.0000
Epoch [8800/10000], Loss: 1837379456.0000
Epoch [8810/10000], Loss: 1833959040.0000
Epoch [8820/10000], Loss: 1861201792.0000
Epoch [8830/10000], Loss: 1825754240.0000
Epoch [8840/10000], Loss: 1834425856.0000
Epoch [8850/10000], Loss: 1828756096.0000
Epoch [8860/10000], Loss: 1827217920.0000
Epoch [8870/10000], Loss: 1826100224.0000
Epoch [8880/10000], Loss: 1837380352.0000
Epoch [8890/10000], Loss: 1833058560.0000
Epoch [8900/10000], Loss: 1817696512.0000
Epoch [8910/10000], Loss: 1820902016.0000
Epoch [8920/10000], Loss: 1827321088.0000
Epoch [8930/10000], Loss: 1839978880.0000
Epoch [8940/10000], Loss: 1816458496.0000
Epoch [8950/10000], Loss: 1813110144.0000
Epoch [8960/10000], Loss: 1810810368.0000
Epoch [8970/10000], Loss: 1810064896.0000
Epoch [8980/10000], Loss: 1818519040.0000
Epoch [8990/10000], Loss: 1811172736.0000
Epoch [9000/10000], Loss: 1811548160.0000
Epoch [9010/10000], Loss: 1809094400.0000
Epoch [9020/10000], Loss: 1806740480.0000
Epoch [9030/10000], Loss: 1810307200.0000
Epoch [9040/10000], Loss: 1801981184.0000
Epoch [9050/10000], Loss: 1806774400.0000
Epoch [9060/10000], Loss: 1801376768.0000
Epoch [9070/10000], Loss: 1797924864.0000
Epoch [9080/10000], Loss: 1810909056.0000
Epoch [9090/10000], Loss: 1789628544.0000
Epoch [9100/10000], Loss: 1808957568.0000
Epoch [9110/10000], Loss: 1784388608.0000
Epoch [9120/10000], Loss: 1795287040.0000
Epoch [9130/10000], Loss: 1786632064.0000
Epoch [9140/10000], Loss: 1821871360.0000
Epoch [9150/10000], Loss: 1791533952.0000
Epoch [9160/10000], Loss: 1783282176.0000
Epoch [9170/10000], Loss: 1783583744.0000
Epoch [9180/10000], Loss: 1782998528.0000
Epoch [9190/10000], Loss: 1776673408.0000
Epoch [9200/10000], Loss: 1796944512.0000
Epoch [9210/10000], Loss: 1778765184.0000
Epoch [9220/10000], Loss: 1781335808.0000
Epoch [9230/10000], Loss: 1770808576.0000
Epoch [9240/10000], Loss: 1779689856.0000
Epoch [9250/10000], Loss: 1769881856.0000
Epoch [9260/10000], Loss: 1781874688.0000
Epoch [9270/10000], Loss: 1762339840.0000
Epoch [9280/10000], Loss: 1798985984.0000
Epoch [9290/10000], Loss: 1760763776.0000
Epoch [9300/10000], Loss: 1758655104.0000
Epoch [9310/10000], Loss: 1759983488.0000
Epoch [9320/10000], Loss: 1761568768.0000
Epoch [9330/10000], Loss: 1764603264.0000
Epoch [9340/10000], Loss: 1764026112.0000
Epoch [9350/10000], Loss: 1764180992.0000
Epoch [9360/10000], Loss: 1750164096.0000
Epoch [9370/10000], Loss: 1762139904.0000
Epoch [9380/10000], Loss: 1759090688.0000
Epoch [9390/10000], Loss: 1771548800.0000
Epoch [9400/10000], Loss: 1757949184.0000
Epoch [9410/10000], Loss: 1766415232.0000
Epoch [9420/10000], Loss: 1743226112.0000
Epoch [9430/10000], Loss: 1747860224.0000
Epoch [9440/10000], Loss: 1755789696.0000
Epoch [9450/10000], Loss: 1746394624.0000
Epoch [9460/10000], Loss: 1739603328.0000
Epoch [9470/10000], Loss: 1737912576.0000
Epoch [9480/10000], Loss: 1776872576.0000
Epoch [9490/10000], Loss: 1761099392.0000
Epoch [9500/10000], Loss: 1736221312.0000
Epoch [9510/10000], Loss: 1729684864.0000
Epoch [9520/10000], Loss: 1736658816.0000
Epoch [9530/10000], Loss: 1747777792.0000
Epoch [9540/10000], Loss: 1748763392.0000
Epoch [9550/10000], Loss: 1732537856.0000
Epoch [9560/10000], Loss: 1730911488.0000
Epoch [9570/10000], Loss: 1723521664.0000
Epoch [9580/10000], Loss: 1739661184.0000
Epoch [9590/10000], Loss: 1719809536.0000
Epoch [9600/10000], Loss: 1736199808.0000
Epoch [9610/10000], Loss: 1718024576.0000
Epoch [9620/10000], Loss: 1753310848.0000
Epoch [9630/10000], Loss: 1738170624.0000
Epoch [9640/10000], Loss: 1724782976.0000
Epoch [9650/10000], Loss: 1719633024.0000
Epoch [9660/10000], Loss: 1712000512.0000
Epoch [9670/10000], Loss: 1722330624.0000
Epoch [9680/10000], Loss: 1708906496.0000
Epoch [9690/10000], Loss: 1720066944.0000
Epoch [9700/10000], Loss: 1710928384.0000
Epoch [9710/10000], Loss: 1718964864.0000
Epoch [9720/10000], Loss: 1721799424.0000
Epoch [9730/10000], Loss: 1723724032.0000
Epoch [9740/10000], Loss: 1705203328.0000
Epoch [9750/10000], Loss: 1703469824.0000
Epoch [9760/10000], Loss: 1701836800.0000
Epoch [9770/10000], Loss: 1714315392.0000
Epoch [9780/10000], Loss: 1695794304.0000
Epoch [9790/10000], Loss: 1718911104.0000
Epoch [9800/10000], Loss: 1745809664.0000
Epoch [9810/10000], Loss: 1700119680.0000
Epoch [9820/10000], Loss: 1690125312.0000
Epoch [9830/10000], Loss: 1691023232.0000
Epoch [9840/10000], Loss: 1693270912.0000
Epoch [9850/10000], Loss: 1694837120.0000
Epoch [9860/10000], Loss: 1698649600.0000
Epoch [9870/10000], Loss: 1694360064.0000
Epoch [9880/10000], Loss: 1691333120.0000
Epoch [9890/10000], Loss: 1700033408.0000
Epoch [9900/10000], Loss: 1694980608.0000
Epoch [9910/10000], Loss: 1682358400.0000
Epoch [9920/10000], Loss: 1700345088.0000
Epoch [9930/10000], Loss: 1684906368.0000
Epoch [9940/10000], Loss: 1689115776.0000
Epoch [9950/10000], Loss: 1684757888.0000
Epoch [9960/10000], Loss: 1678440704.0000
Epoch [9970/10000], Loss: 1704780928.0000
Epoch [9980/10000], Loss: 1678669952.0000
Epoch [9990/10000], Loss: 1676608896.0000
Epoch [10000/10000], Loss: 1678169216.0000
Test Loss: 23384637440.0000
Training time: 23.09 seconds
In [39]:
#Trimming it down to what we know is relevant
Y = data['price']
X = data.drop(['id', 'date', 'price','condition', 'yr_built', 'yr_renovated', 'lat', 'long','house_age','living percentage','price_per_sqft_living', 'price_per_sqft_lot', 'years_since_renovation', 'sqft_living15', 'sqft_lot15', 'sqft_lot', 'Season'], axis=1)
random_state = 42

X_train, X_test, Y_train, Y_test = train_test_split(X, Y, random_state = random_state, shuffle = True)
print(X_train.columns)
Index(['bedrooms', 'bathrooms', 'sqft_living', 'floors', 'waterfront', 'view',
       'grade', 'sqft_above', 'sqft_basement', 'zipcode', 'num_rooms'],
      dtype='object')
In [40]:
#Converting to numpy arrays
X_train = X_train.values
X_test = X_test.values
Y_train = Y_train.values
Y_test = Y_test.values

#Normalizing features
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

#Converting to PyTorch tensors
X_train = torch.tensor(X_train, dtype=torch.float32).to(device)
X_test = torch.tensor(X_test, dtype=torch.float32).to(device)
Y_train = torch.tensor(Y_train, dtype=torch.float32).view(-1, 1).to(device)
Y_test = torch.tensor(Y_test, dtype=torch.float32).view(-1, 1).to(device)

start_time = time.time()

class HousePricePredictor(nn.Module):
    def __init__(self, input_size):
        super(HousePricePredictor, self).__init__()
        self.fc0 = nn.Linear(input_size, 512)
        self.fc1 = nn.Linear(512, 256)
        self.fc2 = nn.Linear(256, 128)
        self.fc3 = nn.Linear(128, 64)
        self.fc4 = nn.Linear(64, 1)
        
        
    def forward(self, x):
        x = torch.relu(self.fc0(x))
        x = torch.relu(self.fc1(x))
        x = torch.relu(self.fc2(x))
        x = torch.relu(self.fc3(x))
        x = self.fc4(x)
        return x

input_size = X_train.shape[1]
model = HousePricePredictor(input_size).to(device)

#training loop
criterion = nn.MSELoss()
optimizer = optim.Adam(model.parameters(), lr=0.001)
train_losses = []
num_epochs = 10000
for epoch in range(num_epochs):
    model.train()
    optimizer.zero_grad()
    outputs = model(X_train)
    loss = criterion(outputs, Y_train)
    loss.backward()
    optimizer.step()
    train_losses.append(loss.item())
    
    if (epoch+1) % 10 == 0:
        print(f'Epoch [{epoch+1}/{num_epochs}], Loss: {loss.item():.4f}')

#Evaluating the model
model.eval()
with torch.no_grad():
    predictions = model(X_test)
    test_loss = criterion(predictions, Y_test)
    print(f'Test Loss: {test_loss.item():.4f}')

end_time = time.time()
training_time = end_time - start_time
print(f"Training time: {training_time:.2f} seconds")

plt.plot(range(num_epochs), train_losses, label='Training Losses')
plt.xlabel('Epoch')
plt.ylabel('Loss')
plt.title('Training Loss Curve')
plt.legend()
plt.show()
Epoch [10/10000], Loss: 433123753984.0000
Epoch [20/10000], Loss: 433085906944.0000
Epoch [30/10000], Loss: 432908173312.0000
Epoch [40/10000], Loss: 432290594816.0000
Epoch [50/10000], Loss: 430519877632.0000
Epoch [60/10000], Loss: 426108354560.0000
Epoch [70/10000], Loss: 416304168960.0000
Epoch [80/10000], Loss: 396611158016.0000
Epoch [90/10000], Loss: 360817459200.0000
Epoch [100/10000], Loss: 302777106432.0000
Epoch [110/10000], Loss: 222353539072.0000
Epoch [120/10000], Loss: 137843884032.0000
Epoch [130/10000], Loss: 92328861696.0000
Epoch [140/10000], Loss: 91405885440.0000
Epoch [150/10000], Loss: 85511929856.0000
Epoch [160/10000], Loss: 81505902592.0000
Epoch [170/10000], Loss: 78983544832.0000
Epoch [180/10000], Loss: 76222545920.0000
Epoch [190/10000], Loss: 73866297344.0000
Epoch [200/10000], Loss: 71644569600.0000
Epoch [210/10000], Loss: 69584281600.0000
Epoch [220/10000], Loss: 67693244416.0000
Epoch [230/10000], Loss: 65963782144.0000
Epoch [240/10000], Loss: 64397950976.0000
Epoch [250/10000], Loss: 62984855552.0000
Epoch [260/10000], Loss: 61716807680.0000
Epoch [270/10000], Loss: 60585517056.0000
Epoch [280/10000], Loss: 59581640704.0000
Epoch [290/10000], Loss: 58691244032.0000
Epoch [300/10000], Loss: 57902153728.0000
Epoch [310/10000], Loss: 57202495488.0000
Epoch [320/10000], Loss: 56581398528.0000
Epoch [330/10000], Loss: 56030064640.0000
Epoch [340/10000], Loss: 55539490816.0000
Epoch [350/10000], Loss: 55101911040.0000
Epoch [360/10000], Loss: 54709227520.0000
Epoch [370/10000], Loss: 54354247680.0000
Epoch [380/10000], Loss: 54032269312.0000
Epoch [390/10000], Loss: 53738221568.0000
Epoch [400/10000], Loss: 53469122560.0000
Epoch [410/10000], Loss: 53221863424.0000
Epoch [420/10000], Loss: 52992192512.0000
Epoch [430/10000], Loss: 52778631168.0000
Epoch [440/10000], Loss: 52579926016.0000
Epoch [450/10000], Loss: 52393545728.0000
Epoch [460/10000], Loss: 52218216448.0000
Epoch [470/10000], Loss: 52053381120.0000
Epoch [480/10000], Loss: 51897520128.0000
Epoch [490/10000], Loss: 51749773312.0000
Epoch [500/10000], Loss: 51609300992.0000
Epoch [510/10000], Loss: 51475271680.0000
Epoch [520/10000], Loss: 51347415040.0000
Epoch [530/10000], Loss: 51225006080.0000
Epoch [540/10000], Loss: 51106701312.0000
Epoch [550/10000], Loss: 50992160768.0000
Epoch [560/10000], Loss: 50881916928.0000
Epoch [570/10000], Loss: 50775461888.0000
Epoch [580/10000], Loss: 50672455680.0000
Epoch [590/10000], Loss: 50573135872.0000
Epoch [600/10000], Loss: 50476826624.0000
Epoch [610/10000], Loss: 50383405056.0000
Epoch [620/10000], Loss: 50292948992.0000
Epoch [630/10000], Loss: 50205278208.0000
Epoch [640/10000], Loss: 50120241152.0000
Epoch [650/10000], Loss: 50038005760.0000
Epoch [660/10000], Loss: 49958199296.0000
Epoch [670/10000], Loss: 49880924160.0000
Epoch [680/10000], Loss: 49806135296.0000
Epoch [690/10000], Loss: 49733861376.0000
Epoch [700/10000], Loss: 49663827968.0000
Epoch [710/10000], Loss: 49595822080.0000
Epoch [720/10000], Loss: 49529806848.0000
Epoch [730/10000], Loss: 49465511936.0000
Epoch [740/10000], Loss: 49402994688.0000
Epoch [750/10000], Loss: 49342222336.0000
Epoch [760/10000], Loss: 49282969600.0000
Epoch [770/10000], Loss: 49225150464.0000
Epoch [780/10000], Loss: 49168609280.0000
Epoch [790/10000], Loss: 49113288704.0000
Epoch [800/10000], Loss: 49059307520.0000
Epoch [810/10000], Loss: 49006460928.0000
Epoch [820/10000], Loss: 48954724352.0000
Epoch [830/10000], Loss: 48903892992.0000
Epoch [840/10000], Loss: 48853954560.0000
Epoch [850/10000], Loss: 48805195776.0000
Epoch [860/10000], Loss: 48757596160.0000
Epoch [870/10000], Loss: 48710979584.0000
Epoch [880/10000], Loss: 48665198592.0000
Epoch [890/10000], Loss: 48620236800.0000
Epoch [900/10000], Loss: 48575926272.0000
Epoch [910/10000], Loss: 48531972096.0000
Epoch [920/10000], Loss: 48488517632.0000
Epoch [930/10000], Loss: 48445558784.0000
Epoch [940/10000], Loss: 48403062784.0000
Epoch [950/10000], Loss: 48361123840.0000
Epoch [960/10000], Loss: 48319639552.0000
Epoch [970/10000], Loss: 48278495232.0000
Epoch [980/10000], Loss: 48237621248.0000
Epoch [990/10000], Loss: 48196780032.0000
Epoch [1000/10000], Loss: 48156098560.0000
Epoch [1010/10000], Loss: 48115376128.0000
Epoch [1020/10000], Loss: 48074670080.0000
Epoch [1030/10000], Loss: 48034029568.0000
Epoch [1040/10000], Loss: 47993475072.0000
Epoch [1050/10000], Loss: 47952949248.0000
Epoch [1060/10000], Loss: 47912316928.0000
Epoch [1070/10000], Loss: 47871500288.0000
Epoch [1080/10000], Loss: 47830519808.0000
Epoch [1090/10000], Loss: 47789236224.0000
Epoch [1100/10000], Loss: 47747649536.0000
Epoch [1110/10000], Loss: 47705694208.0000
Epoch [1120/10000], Loss: 47663353856.0000
Epoch [1130/10000], Loss: 47620759552.0000
Epoch [1140/10000], Loss: 47577899008.0000
Epoch [1150/10000], Loss: 47534641152.0000
Epoch [1160/10000], Loss: 47490953216.0000
Epoch [1170/10000], Loss: 47446777856.0000
Epoch [1180/10000], Loss: 47402016768.0000
Epoch [1190/10000], Loss: 47356772352.0000
Epoch [1200/10000], Loss: 47310921728.0000
Epoch [1210/10000], Loss: 47264571392.0000
Epoch [1220/10000], Loss: 47217758208.0000
Epoch [1230/10000], Loss: 47170416640.0000
Epoch [1240/10000], Loss: 47122608128.0000
Epoch [1250/10000], Loss: 47074250752.0000
Epoch [1260/10000], Loss: 47025512448.0000
Epoch [1270/10000], Loss: 46976401408.0000
Epoch [1280/10000], Loss: 46927015936.0000
Epoch [1290/10000], Loss: 46877319168.0000
Epoch [1300/10000], Loss: 46827229184.0000
Epoch [1310/10000], Loss: 46776819712.0000
Epoch [1320/10000], Loss: 46726045696.0000
Epoch [1330/10000], Loss: 46674935808.0000
Epoch [1340/10000], Loss: 46623571968.0000
Epoch [1350/10000], Loss: 46571896832.0000
Epoch [1360/10000], Loss: 46520197120.0000
Epoch [1370/10000], Loss: 46468505600.0000
Epoch [1380/10000], Loss: 46416666624.0000
Epoch [1390/10000], Loss: 46364721152.0000
Epoch [1400/10000], Loss: 46312660992.0000
Epoch [1410/10000], Loss: 46260436992.0000
Epoch [1420/10000], Loss: 46207950848.0000
Epoch [1430/10000], Loss: 46155329536.0000
Epoch [1440/10000], Loss: 46102659072.0000
Epoch [1450/10000], Loss: 46049714176.0000
Epoch [1460/10000], Loss: 45996560384.0000
Epoch [1470/10000], Loss: 45943492608.0000
Epoch [1480/10000], Loss: 45890469888.0000
Epoch [1490/10000], Loss: 45837217792.0000
Epoch [1500/10000], Loss: 45783986176.0000
Epoch [1510/10000], Loss: 45730725888.0000
Epoch [1520/10000], Loss: 45677473792.0000
Epoch [1530/10000], Loss: 45624205312.0000
Epoch [1540/10000], Loss: 45570584576.0000
Epoch [1550/10000], Loss: 45516656640.0000
Epoch [1560/10000], Loss: 45462568960.0000
Epoch [1570/10000], Loss: 45408366592.0000
Epoch [1580/10000], Loss: 45354106880.0000
Epoch [1590/10000], Loss: 45299748864.0000
Epoch [1600/10000], Loss: 45245194240.0000
Epoch [1610/10000], Loss: 45190438912.0000
Epoch [1620/10000], Loss: 45135618048.0000
Epoch [1630/10000], Loss: 45080973312.0000
Epoch [1640/10000], Loss: 45026299904.0000
Epoch [1650/10000], Loss: 44971798528.0000
Epoch [1660/10000], Loss: 44917346304.0000
Epoch [1670/10000], Loss: 44862742528.0000
Epoch [1680/10000], Loss: 44808183808.0000
Epoch [1690/10000], Loss: 44753489920.0000
Epoch [1700/10000], Loss: 44698550272.0000
Epoch [1710/10000], Loss: 44643352576.0000
Epoch [1720/10000], Loss: 44588212224.0000
Epoch [1730/10000], Loss: 44532850688.0000
Epoch [1740/10000], Loss: 44476874752.0000
Epoch [1750/10000], Loss: 44420567040.0000
Epoch [1760/10000], Loss: 44365099008.0000
Epoch [1770/10000], Loss: 44309479424.0000
Epoch [1780/10000], Loss: 44253646848.0000
Epoch [1790/10000], Loss: 44197101568.0000
Epoch [1800/10000], Loss: 44139503616.0000
Epoch [1810/10000], Loss: 44081954816.0000
Epoch [1820/10000], Loss: 44024471552.0000
Epoch [1830/10000], Loss: 43966869504.0000
Epoch [1840/10000], Loss: 43908521984.0000
Epoch [1850/10000], Loss: 43849953280.0000
Epoch [1860/10000], Loss: 43791216640.0000
Epoch [1870/10000], Loss: 43732287488.0000
Epoch [1880/10000], Loss: 43673018368.0000
Epoch [1890/10000], Loss: 43613114368.0000
Epoch [1900/10000], Loss: 43552575488.0000
Epoch [1910/10000], Loss: 43491168256.0000
Epoch [1920/10000], Loss: 43428966400.0000
Epoch [1930/10000], Loss: 43366498304.0000
Epoch [1940/10000], Loss: 43305971712.0000
Epoch [1950/10000], Loss: 43244978176.0000
Epoch [1960/10000], Loss: 43183398912.0000
Epoch [1970/10000], Loss: 43121479680.0000
Epoch [1980/10000], Loss: 43058610176.0000
Epoch [1990/10000], Loss: 42994343936.0000
Epoch [2000/10000], Loss: 42928746496.0000
Epoch [2010/10000], Loss: 42863177728.0000
Epoch [2020/10000], Loss: 42798022656.0000
Epoch [2030/10000], Loss: 42732965888.0000
Epoch [2040/10000], Loss: 42666950656.0000
Epoch [2050/10000], Loss: 42601414656.0000
Epoch [2060/10000], Loss: 42535682048.0000
Epoch [2070/10000], Loss: 42469240832.0000
Epoch [2080/10000], Loss: 42403065856.0000
Epoch [2090/10000], Loss: 42337288192.0000
Epoch [2100/10000], Loss: 42271580160.0000
Epoch [2110/10000], Loss: 42205184000.0000
Epoch [2120/10000], Loss: 42138931200.0000
Epoch [2130/10000], Loss: 42071752704.0000
Epoch [2140/10000], Loss: 42003578880.0000
Epoch [2150/10000], Loss: 41934082048.0000
Epoch [2160/10000], Loss: 41862565888.0000
Epoch [2170/10000], Loss: 41791700992.0000
Epoch [2180/10000], Loss: 41721675776.0000
Epoch [2190/10000], Loss: 41651695616.0000
Epoch [2200/10000], Loss: 41581367296.0000
Epoch [2210/10000], Loss: 41511755776.0000
Epoch [2220/10000], Loss: 41443069952.0000
Epoch [2230/10000], Loss: 41375137792.0000
Epoch [2240/10000], Loss: 41309499392.0000
Epoch [2250/10000], Loss: 41245118464.0000
Epoch [2260/10000], Loss: 41182224384.0000
Epoch [2270/10000], Loss: 41119899648.0000
Epoch [2280/10000], Loss: 41058168832.0000
Epoch [2290/10000], Loss: 40997515264.0000
Epoch [2300/10000], Loss: 40937549824.0000
Epoch [2310/10000], Loss: 40877572096.0000
Epoch [2320/10000], Loss: 40817364992.0000
Epoch [2330/10000], Loss: 40756547584.0000
Epoch [2340/10000], Loss: 40695144448.0000
Epoch [2350/10000], Loss: 40633778176.0000
Epoch [2360/10000], Loss: 40571150336.0000
Epoch [2370/10000], Loss: 40508354560.0000
Epoch [2380/10000], Loss: 40446668800.0000
Epoch [2390/10000], Loss: 40385581056.0000
Epoch [2400/10000], Loss: 40325083136.0000
Epoch [2410/10000], Loss: 40263995392.0000
Epoch [2420/10000], Loss: 40202272768.0000
Epoch [2430/10000], Loss: 40141389824.0000
Epoch [2440/10000], Loss: 40079626240.0000
Epoch [2450/10000], Loss: 40017772544.0000
Epoch [2460/10000], Loss: 39954550784.0000
Epoch [2470/10000], Loss: 39891140608.0000
Epoch [2480/10000], Loss: 39827517440.0000
Epoch [2490/10000], Loss: 39763283968.0000
Epoch [2500/10000], Loss: 39697616896.0000
Epoch [2510/10000], Loss: 39632187392.0000
Epoch [2520/10000], Loss: 39567339520.0000
Epoch [2530/10000], Loss: 39501819904.0000
Epoch [2540/10000], Loss: 39436402688.0000
Epoch [2550/10000], Loss: 39370784768.0000
Epoch [2560/10000], Loss: 39306240000.0000
Epoch [2570/10000], Loss: 39243235328.0000
Epoch [2580/10000], Loss: 39180664832.0000
Epoch [2590/10000], Loss: 39117889536.0000
Epoch [2600/10000], Loss: 39055564800.0000
Epoch [2610/10000], Loss: 38993301504.0000
Epoch [2620/10000], Loss: 38931697664.0000
Epoch [2630/10000], Loss: 38869135360.0000
Epoch [2640/10000], Loss: 38807162880.0000
Epoch [2650/10000], Loss: 38746361856.0000
Epoch [2660/10000], Loss: 38685904896.0000
Epoch [2670/10000], Loss: 38625583104.0000
Epoch [2680/10000], Loss: 38564761600.0000
Epoch [2690/10000], Loss: 38502772736.0000
Epoch [2700/10000], Loss: 38440820736.0000
Epoch [2710/10000], Loss: 38378803200.0000
Epoch [2720/10000], Loss: 38316101632.0000
Epoch [2730/10000], Loss: 38252744704.0000
Epoch [2740/10000], Loss: 38189580288.0000
Epoch [2750/10000], Loss: 38126247936.0000
Epoch [2760/10000], Loss: 38062063616.0000
Epoch [2770/10000], Loss: 37998301184.0000
Epoch [2780/10000], Loss: 37935026176.0000
Epoch [2790/10000], Loss: 37870981120.0000
Epoch [2800/10000], Loss: 37807476736.0000
Epoch [2810/10000], Loss: 37744279552.0000
Epoch [2820/10000], Loss: 37681082368.0000
Epoch [2830/10000], Loss: 37617844224.0000
Epoch [2840/10000], Loss: 37554446336.0000
Epoch [2850/10000], Loss: 37491601408.0000
Epoch [2860/10000], Loss: 37429387264.0000
Epoch [2870/10000], Loss: 37367332864.0000
Epoch [2880/10000], Loss: 37304868864.0000
Epoch [2890/10000], Loss: 37243310080.0000
Epoch [2900/10000], Loss: 37182840832.0000
Epoch [2910/10000], Loss: 37120557056.0000
Epoch [2920/10000], Loss: 37057081344.0000
Epoch [2930/10000], Loss: 36993789952.0000
Epoch [2940/10000], Loss: 36931321856.0000
Epoch [2950/10000], Loss: 36870520832.0000
Epoch [2960/10000], Loss: 36808220672.0000
Epoch [2970/10000], Loss: 36745846784.0000
Epoch [2980/10000], Loss: 36683567104.0000
Epoch [2990/10000], Loss: 36621447168.0000
Epoch [3000/10000], Loss: 36558647296.0000
Epoch [3010/10000], Loss: 36495294464.0000
Epoch [3020/10000], Loss: 36430897152.0000
Epoch [3030/10000], Loss: 36365135872.0000
Epoch [3040/10000], Loss: 36299333632.0000
Epoch [3050/10000], Loss: 36233932800.0000
Epoch [3060/10000], Loss: 36168835072.0000
Epoch [3070/10000], Loss: 36103720960.0000
Epoch [3080/10000], Loss: 36038590464.0000
Epoch [3090/10000], Loss: 35972071424.0000
Epoch [3100/10000], Loss: 35903279104.0000
Epoch [3110/10000], Loss: 35831713792.0000
Epoch [3120/10000], Loss: 35760906240.0000
Epoch [3130/10000], Loss: 35690352640.0000
Epoch [3140/10000], Loss: 35623174144.0000
Epoch [3150/10000], Loss: 35557777408.0000
Epoch [3160/10000], Loss: 35492593664.0000
Epoch [3170/10000], Loss: 35429822464.0000
Epoch [3180/10000], Loss: 35368087552.0000
Epoch [3190/10000], Loss: 35304632320.0000
Epoch [3200/10000], Loss: 35239518208.0000
Epoch [3210/10000], Loss: 35175227392.0000
Epoch [3220/10000], Loss: 35111505920.0000
Epoch [3230/10000], Loss: 35048902656.0000
Epoch [3240/10000], Loss: 34986418176.0000
Epoch [3250/10000], Loss: 34924318720.0000
Epoch [3260/10000], Loss: 34864910336.0000
Epoch [3270/10000], Loss: 34805055488.0000
Epoch [3280/10000], Loss: 34743554048.0000
Epoch [3290/10000], Loss: 34681892864.0000
Epoch [3300/10000], Loss: 34618687488.0000
Epoch [3310/10000], Loss: 34556387328.0000
Epoch [3320/10000], Loss: 34497523712.0000
Epoch [3330/10000], Loss: 34439299072.0000
Epoch [3340/10000], Loss: 34380333056.0000
Epoch [3350/10000], Loss: 34319366144.0000
Epoch [3360/10000], Loss: 34259963904.0000
Epoch [3370/10000], Loss: 34201683968.0000
Epoch [3380/10000], Loss: 34144407552.0000
Epoch [3390/10000], Loss: 34088597504.0000
Epoch [3400/10000], Loss: 34032793600.0000
Epoch [3410/10000], Loss: 33975797760.0000
Epoch [3420/10000], Loss: 33919277056.0000
Epoch [3430/10000], Loss: 33862860800.0000
Epoch [3440/10000], Loss: 33807140864.0000
Epoch [3450/10000], Loss: 33751066624.0000
Epoch [3460/10000], Loss: 33694214144.0000
Epoch [3470/10000], Loss: 33636380672.0000
Epoch [3480/10000], Loss: 33579370496.0000
Epoch [3490/10000], Loss: 33520928768.0000
Epoch [3500/10000], Loss: 33462120448.0000
Epoch [3510/10000], Loss: 33401196544.0000
Epoch [3520/10000], Loss: 33339387904.0000
Epoch [3530/10000], Loss: 33278212096.0000
Epoch [3540/10000], Loss: 33218537472.0000
Epoch [3550/10000], Loss: 33159372800.0000
Epoch [3560/10000], Loss: 33101731840.0000
Epoch [3570/10000], Loss: 33043058688.0000
Epoch [3580/10000], Loss: 32982636544.0000
Epoch [3590/10000], Loss: 32921874432.0000
Epoch [3600/10000], Loss: 32861376512.0000
Epoch [3610/10000], Loss: 32797163520.0000
Epoch [3620/10000], Loss: 32736786432.0000
Epoch [3630/10000], Loss: 32677056512.0000
Epoch [3640/10000], Loss: 32617498624.0000
Epoch [3650/10000], Loss: 32556343296.0000
Epoch [3660/10000], Loss: 32496867328.0000
Epoch [3670/10000], Loss: 32434368512.0000
Epoch [3680/10000], Loss: 32375412736.0000
Epoch [3690/10000], Loss: 32316981248.0000
Epoch [3700/10000], Loss: 32256516096.0000
Epoch [3710/10000], Loss: 32193832960.0000
Epoch [3720/10000], Loss: 32137531392.0000
Epoch [3730/10000], Loss: 32075558912.0000
Epoch [3740/10000], Loss: 32009701376.0000
Epoch [3750/10000], Loss: 31946993664.0000
Epoch [3760/10000], Loss: 31891560448.0000
Epoch [3770/10000], Loss: 31835664384.0000
Epoch [3780/10000], Loss: 31774582784.0000
Epoch [3790/10000], Loss: 31715045376.0000
Epoch [3800/10000], Loss: 31661099008.0000
Epoch [3810/10000], Loss: 31604490240.0000
Epoch [3820/10000], Loss: 31540146176.0000
Epoch [3830/10000], Loss: 31480018944.0000
Epoch [3840/10000], Loss: 31423313920.0000
Epoch [3850/10000], Loss: 31360931840.0000
Epoch [3860/10000], Loss: 31293685760.0000
Epoch [3870/10000], Loss: 31236620288.0000
Epoch [3880/10000], Loss: 31176226816.0000
Epoch [3890/10000], Loss: 31112638464.0000
Epoch [3900/10000], Loss: 31065583616.0000
Epoch [3910/10000], Loss: 31001249792.0000
Epoch [3920/10000], Loss: 30939500544.0000
Epoch [3930/10000], Loss: 30876381184.0000
Epoch [3940/10000], Loss: 30812821504.0000
Epoch [3950/10000], Loss: 30752745472.0000
Epoch [3960/10000], Loss: 30698539008.0000
Epoch [3970/10000], Loss: 30631655424.0000
Epoch [3980/10000], Loss: 30567356416.0000
Epoch [3990/10000], Loss: 30507431936.0000
Epoch [4000/10000], Loss: 30456631296.0000
Epoch [4010/10000], Loss: 30389622784.0000
Epoch [4020/10000], Loss: 30322411520.0000
Epoch [4030/10000], Loss: 30277322752.0000
Epoch [4040/10000], Loss: 30211627008.0000
Epoch [4050/10000], Loss: 30141956096.0000
Epoch [4060/10000], Loss: 30083686400.0000
Epoch [4070/10000], Loss: 30024067072.0000
Epoch [4080/10000], Loss: 29963767808.0000
Epoch [4090/10000], Loss: 29893201920.0000
Epoch [4100/10000], Loss: 29829593088.0000
Epoch [4110/10000], Loss: 29776230400.0000
Epoch [4120/10000], Loss: 29719533568.0000
Epoch [4130/10000], Loss: 29653594112.0000
Epoch [4140/10000], Loss: 29584039936.0000
Epoch [4150/10000], Loss: 29523994624.0000
Epoch [4160/10000], Loss: 29469421568.0000
Epoch [4170/10000], Loss: 29409118208.0000
Epoch [4180/10000], Loss: 29336248320.0000
Epoch [4190/10000], Loss: 29269356544.0000
Epoch [4200/10000], Loss: 29212248064.0000
Epoch [4210/10000], Loss: 29156270080.0000
Epoch [4220/10000], Loss: 29085296640.0000
Epoch [4230/10000], Loss: 29024149504.0000
Epoch [4240/10000], Loss: 28974002176.0000
Epoch [4250/10000], Loss: 28925597696.0000
Epoch [4260/10000], Loss: 28864735232.0000
Epoch [4270/10000], Loss: 28797915136.0000
Epoch [4280/10000], Loss: 28733919232.0000
Epoch [4290/10000], Loss: 28697649152.0000
Epoch [4300/10000], Loss: 28636053504.0000
Epoch [4310/10000], Loss: 28572121088.0000
Epoch [4320/10000], Loss: 28507367424.0000
Epoch [4330/10000], Loss: 28454770688.0000
Epoch [4340/10000], Loss: 28409169920.0000
Epoch [4350/10000], Loss: 28340058112.0000
Epoch [4360/10000], Loss: 28274032640.0000
Epoch [4370/10000], Loss: 28232183808.0000
Epoch [4380/10000], Loss: 28180299776.0000
Epoch [4390/10000], Loss: 28109682688.0000
Epoch [4400/10000], Loss: 28048709632.0000
Epoch [4410/10000], Loss: 28001058816.0000
Epoch [4420/10000], Loss: 27958376448.0000
Epoch [4430/10000], Loss: 27908364288.0000
Epoch [4440/10000], Loss: 27848321024.0000
Epoch [4450/10000], Loss: 27789520896.0000
Epoch [4460/10000], Loss: 27734818816.0000
Epoch [4470/10000], Loss: 27684968448.0000
Epoch [4480/10000], Loss: 27656052736.0000
Epoch [4490/10000], Loss: 27598372864.0000
Epoch [4500/10000], Loss: 27539243008.0000
Epoch [4510/10000], Loss: 27480328192.0000
Epoch [4520/10000], Loss: 27434561536.0000
Epoch [4530/10000], Loss: 27393921024.0000
Epoch [4540/10000], Loss: 27355652096.0000
Epoch [4550/10000], Loss: 27295070208.0000
Epoch [4560/10000], Loss: 27239047168.0000
Epoch [4570/10000], Loss: 27186755584.0000
Epoch [4580/10000], Loss: 27148347392.0000
Epoch [4590/10000], Loss: 27109529600.0000
Epoch [4600/10000], Loss: 27064543232.0000
Epoch [4610/10000], Loss: 27008882688.0000
Epoch [4620/10000], Loss: 26949349376.0000
Epoch [4630/10000], Loss: 26898837504.0000
Epoch [4640/10000], Loss: 26867986432.0000
Epoch [4650/10000], Loss: 26833250304.0000
Epoch [4660/10000], Loss: 26776686592.0000
Epoch [4670/10000], Loss: 26717870080.0000
Epoch [4680/10000], Loss: 26670292992.0000
Epoch [4690/10000], Loss: 26643503104.0000
Epoch [4700/10000], Loss: 26604355584.0000
Epoch [4710/10000], Loss: 26548557824.0000
Epoch [4720/10000], Loss: 26485551104.0000
Epoch [4730/10000], Loss: 26433857536.0000
Epoch [4740/10000], Loss: 26397999104.0000
Epoch [4750/10000], Loss: 26370013184.0000
Epoch [4760/10000], Loss: 26320424960.0000
Epoch [4770/10000], Loss: 26262077440.0000
Epoch [4780/10000], Loss: 26210578432.0000
Epoch [4790/10000], Loss: 26166820864.0000
Epoch [4800/10000], Loss: 26157262848.0000
Epoch [4810/10000], Loss: 26109483008.0000
Epoch [4820/10000], Loss: 26050703360.0000
Epoch [4830/10000], Loss: 25996228608.0000
Epoch [4840/10000], Loss: 25972238336.0000
Epoch [4850/10000], Loss: 25938556928.0000
Epoch [4860/10000], Loss: 25878867968.0000
Epoch [4870/10000], Loss: 25826349056.0000
Epoch [4880/10000], Loss: 25803890688.0000
Epoch [4890/10000], Loss: 25777180672.0000
Epoch [4900/10000], Loss: 25723641856.0000
Epoch [4910/10000], Loss: 25667381248.0000
Epoch [4920/10000], Loss: 25623672832.0000
Epoch [4930/10000], Loss: 25594804224.0000
Epoch [4940/10000], Loss: 25577113600.0000
Epoch [4950/10000], Loss: 25536501760.0000
Epoch [4960/10000], Loss: 25483905024.0000
Epoch [4970/10000], Loss: 25432236032.0000
Epoch [4980/10000], Loss: 25400788992.0000
Epoch [4990/10000], Loss: 25399463936.0000
Epoch [5000/10000], Loss: 25354465280.0000
Epoch [5010/10000], Loss: 25298753536.0000
Epoch [5020/10000], Loss: 25250152448.0000
Epoch [5030/10000], Loss: 25219721216.0000
Epoch [5040/10000], Loss: 25206489088.0000
Epoch [5050/10000], Loss: 25181310976.0000
Epoch [5060/10000], Loss: 25143289856.0000
Epoch [5070/10000], Loss: 25105645568.0000
Epoch [5080/10000], Loss: 25065107456.0000
Epoch [5090/10000], Loss: 25017317376.0000
Epoch [5100/10000], Loss: 24972283904.0000
Epoch [5110/10000], Loss: 24934078464.0000
Epoch [5120/10000], Loss: 24906354688.0000
Epoch [5130/10000], Loss: 24890351616.0000
Epoch [5140/10000], Loss: 24861689856.0000
Epoch [5150/10000], Loss: 24822073344.0000
Epoch [5160/10000], Loss: 24769449984.0000
Epoch [5170/10000], Loss: 24722096128.0000
Epoch [5180/10000], Loss: 24680411136.0000
Epoch [5190/10000], Loss: 24644280320.0000
Epoch [5200/10000], Loss: 24640305152.0000
Epoch [5210/10000], Loss: 24611229696.0000
Epoch [5220/10000], Loss: 24576212992.0000
Epoch [5230/10000], Loss: 24525670400.0000
Epoch [5240/10000], Loss: 24477536256.0000
Epoch [5250/10000], Loss: 24428652544.0000
Epoch [5260/10000], Loss: 24393379840.0000
Epoch [5270/10000], Loss: 24374663168.0000
Epoch [5280/10000], Loss: 24358023168.0000
Epoch [5290/10000], Loss: 24311474176.0000
Epoch [5300/10000], Loss: 24251467776.0000
Epoch [5310/10000], Loss: 24207544320.0000
Epoch [5320/10000], Loss: 24184920064.0000
Epoch [5330/10000], Loss: 24181473280.0000
Epoch [5340/10000], Loss: 24149334016.0000
Epoch [5350/10000], Loss: 24094713856.0000
Epoch [5360/10000], Loss: 24038144000.0000
Epoch [5370/10000], Loss: 24008751104.0000
Epoch [5380/10000], Loss: 24007067648.0000
Epoch [5390/10000], Loss: 23989022720.0000
Epoch [5400/10000], Loss: 23936137216.0000
Epoch [5410/10000], Loss: 23888076800.0000
Epoch [5420/10000], Loss: 23839557632.0000
Epoch [5430/10000], Loss: 23802568704.0000
Epoch [5440/10000], Loss: 23784148992.0000
Epoch [5450/10000], Loss: 23778496512.0000
Epoch [5460/10000], Loss: 23737868288.0000
Epoch [5470/10000], Loss: 23682394112.0000
Epoch [5480/10000], Loss: 23641133056.0000
Epoch [5490/10000], Loss: 23635167232.0000
Epoch [5500/10000], Loss: 23615313920.0000
Epoch [5510/10000], Loss: 23576317952.0000
Epoch [5520/10000], Loss: 23510163456.0000
Epoch [5530/10000], Loss: 23474604032.0000
Epoch [5540/10000], Loss: 23489828864.0000
Epoch [5550/10000], Loss: 23448805376.0000
Epoch [5560/10000], Loss: 23392118784.0000
Epoch [5570/10000], Loss: 23345240064.0000
Epoch [5580/10000], Loss: 23338510336.0000
Epoch [5590/10000], Loss: 23346452480.0000
Epoch [5600/10000], Loss: 23292571648.0000
Epoch [5610/10000], Loss: 23244279808.0000
Epoch [5620/10000], Loss: 23198699520.0000
Epoch [5630/10000], Loss: 23177787392.0000
Epoch [5640/10000], Loss: 23179061248.0000
Epoch [5650/10000], Loss: 23157673984.0000
Epoch [5660/10000], Loss: 23101814784.0000
Epoch [5670/10000], Loss: 23057065984.0000
Epoch [5680/10000], Loss: 23042592768.0000
Epoch [5690/10000], Loss: 23030523904.0000
Epoch [5700/10000], Loss: 23006332928.0000
Epoch [5710/10000], Loss: 22985975808.0000
Epoch [5720/10000], Loss: 22942398464.0000
Epoch [5730/10000], Loss: 22890737664.0000
Epoch [5740/10000], Loss: 22862981120.0000
Epoch [5750/10000], Loss: 22876276736.0000
Epoch [5760/10000], Loss: 22856278016.0000
Epoch [5770/10000], Loss: 22817579008.0000
Epoch [5780/10000], Loss: 22786762752.0000
Epoch [5790/10000], Loss: 22741630976.0000
Epoch [5800/10000], Loss: 22696540160.0000
Epoch [5810/10000], Loss: 22655295488.0000
Epoch [5820/10000], Loss: 22647140352.0000
Epoch [5830/10000], Loss: 22642028544.0000
Epoch [5840/10000], Loss: 22609741824.0000
Epoch [5850/10000], Loss: 22594662400.0000
Epoch [5860/10000], Loss: 22555930624.0000
Epoch [5870/10000], Loss: 22519951360.0000
Epoch [5880/10000], Loss: 22462175232.0000
Epoch [5890/10000], Loss: 22442526720.0000
Epoch [5900/10000], Loss: 22455840768.0000
Epoch [5910/10000], Loss: 22420537344.0000
Epoch [5920/10000], Loss: 22374062080.0000
Epoch [5930/10000], Loss: 22322110464.0000
Epoch [5940/10000], Loss: 22295185408.0000
Epoch [5950/10000], Loss: 22311811072.0000
Epoch [5960/10000], Loss: 22297444352.0000
Epoch [5970/10000], Loss: 22250579968.0000
Epoch [5980/10000], Loss: 22194055168.0000
Epoch [5990/10000], Loss: 22153986048.0000
Epoch [6000/10000], Loss: 22153705472.0000
Epoch [6010/10000], Loss: 22156886016.0000
Epoch [6020/10000], Loss: 22102487040.0000
Epoch [6030/10000], Loss: 22055790592.0000
Epoch [6040/10000], Loss: 22018041856.0000
Epoch [6050/10000], Loss: 21989267456.0000
Epoch [6060/10000], Loss: 21983262720.0000
Epoch [6070/10000], Loss: 22000551936.0000
Epoch [6080/10000], Loss: 21943613440.0000
Epoch [6090/10000], Loss: 21884358656.0000
Epoch [6100/10000], Loss: 21851467776.0000
Epoch [6110/10000], Loss: 21861875712.0000
Epoch [6120/10000], Loss: 21857095680.0000
Epoch [6130/10000], Loss: 21820035072.0000
Epoch [6140/10000], Loss: 21757509632.0000
Epoch [6150/10000], Loss: 21715494912.0000
Epoch [6160/10000], Loss: 21709869056.0000
Epoch [6170/10000], Loss: 21712889856.0000
Epoch [6180/10000], Loss: 21690556416.0000
Epoch [6190/10000], Loss: 21640290304.0000
Epoch [6200/10000], Loss: 21584900096.0000
Epoch [6210/10000], Loss: 21557377024.0000
Epoch [6220/10000], Loss: 21553883136.0000
Epoch [6230/10000], Loss: 21552515072.0000
Epoch [6240/10000], Loss: 21537478656.0000
Epoch [6250/10000], Loss: 21478666240.0000
Epoch [6260/10000], Loss: 21425152000.0000
Epoch [6270/10000], Loss: 21430923264.0000
Epoch [6280/10000], Loss: 21445394432.0000
Epoch [6290/10000], Loss: 21419790336.0000
Epoch [6300/10000], Loss: 21365147648.0000
Epoch [6310/10000], Loss: 21307983872.0000
Epoch [6320/10000], Loss: 21264586752.0000
Epoch [6330/10000], Loss: 21295435776.0000
Epoch [6340/10000], Loss: 21276887040.0000
Epoch [6350/10000], Loss: 21208651776.0000
Epoch [6360/10000], Loss: 21159395328.0000
Epoch [6370/10000], Loss: 21134372864.0000
Epoch [6380/10000], Loss: 21152436224.0000
Epoch [6390/10000], Loss: 21161320448.0000
Epoch [6400/10000], Loss: 21102381056.0000
Epoch [6410/10000], Loss: 21041113088.0000
Epoch [6420/10000], Loss: 21004853248.0000
Epoch [6430/10000], Loss: 21010671616.0000
Epoch [6440/10000], Loss: 21028050944.0000
Epoch [6450/10000], Loss: 20985217024.0000
Epoch [6460/10000], Loss: 20929265664.0000
Epoch [6470/10000], Loss: 20880529408.0000
Epoch [6480/10000], Loss: 20860753920.0000
Epoch [6490/10000], Loss: 20870588416.0000
Epoch [6500/10000], Loss: 20866107392.0000
Epoch [6510/10000], Loss: 20820973568.0000
Epoch [6520/10000], Loss: 20758581248.0000
Epoch [6530/10000], Loss: 20745345024.0000
Epoch [6540/10000], Loss: 20797857792.0000
Epoch [6550/10000], Loss: 20734986240.0000
Epoch [6560/10000], Loss: 20675155968.0000
Epoch [6570/10000], Loss: 20629929984.0000
Epoch [6580/10000], Loss: 20602953728.0000
Epoch [6590/10000], Loss: 20619286528.0000
Epoch [6600/10000], Loss: 20622215168.0000
Epoch [6610/10000], Loss: 20546328576.0000
Epoch [6620/10000], Loss: 20503025664.0000
Epoch [6630/10000], Loss: 20510912512.0000
Epoch [6640/10000], Loss: 20550158336.0000
Epoch [6650/10000], Loss: 20508598272.0000
Epoch [6660/10000], Loss: 20478111744.0000
Epoch [6670/10000], Loss: 20414164992.0000
Epoch [6680/10000], Loss: 20355600384.0000
Epoch [6690/10000], Loss: 20424904704.0000
Epoch [6700/10000], Loss: 20400816128.0000
Epoch [6710/10000], Loss: 20339173376.0000
Epoch [6720/10000], Loss: 20272113664.0000
Epoch [6730/10000], Loss: 20252700672.0000
Epoch [6740/10000], Loss: 20299364352.0000
Epoch [6750/10000], Loss: 20241811456.0000
Epoch [6760/10000], Loss: 20185722880.0000
Epoch [6770/10000], Loss: 20145645568.0000
Epoch [6780/10000], Loss: 20135620608.0000
Epoch [6790/10000], Loss: 20172238848.0000
Epoch [6800/10000], Loss: 20104075264.0000
Epoch [6810/10000], Loss: 20049655808.0000
Epoch [6820/10000], Loss: 20037027840.0000
Epoch [6830/10000], Loss: 20053979136.0000
Epoch [6840/10000], Loss: 20055525376.0000
Epoch [6850/10000], Loss: 19988193280.0000
Epoch [6860/10000], Loss: 19937982464.0000
Epoch [6870/10000], Loss: 20016496640.0000
Epoch [6880/10000], Loss: 19917635584.0000
Epoch [6890/10000], Loss: 19866652672.0000
Epoch [6900/10000], Loss: 19846780928.0000
Epoch [6910/10000], Loss: 19836766208.0000
Epoch [6920/10000], Loss: 19849043968.0000
Epoch [6930/10000], Loss: 19842002944.0000
Epoch [6940/10000], Loss: 19795740672.0000
Epoch [6950/10000], Loss: 19729156096.0000
Epoch [6960/10000], Loss: 19709251584.0000
Epoch [6970/10000], Loss: 19713462272.0000
Epoch [6980/10000], Loss: 19719387136.0000
Epoch [6990/10000], Loss: 19674273792.0000
Epoch [7000/10000], Loss: 19610474496.0000
Epoch [7010/10000], Loss: 19618813952.0000
Epoch [7020/10000], Loss: 19652276224.0000
Epoch [7030/10000], Loss: 19626444800.0000
Epoch [7040/10000], Loss: 19583145984.0000
Epoch [7050/10000], Loss: 19515967488.0000
Epoch [7060/10000], Loss: 19482669056.0000
Epoch [7070/10000], Loss: 19533185024.0000
Epoch [7080/10000], Loss: 19483314176.0000
Epoch [7090/10000], Loss: 19408732160.0000
Epoch [7100/10000], Loss: 19429699584.0000
Epoch [7110/10000], Loss: 19467163648.0000
Epoch [7120/10000], Loss: 19432777728.0000
Epoch [7130/10000], Loss: 19375972352.0000
Epoch [7140/10000], Loss: 19316619264.0000
Epoch [7150/10000], Loss: 19271487488.0000
Epoch [7160/10000], Loss: 19321278464.0000
Epoch [7170/10000], Loss: 19308621824.0000
Epoch [7180/10000], Loss: 19229022208.0000
Epoch [7190/10000], Loss: 19183927296.0000
Epoch [7200/10000], Loss: 19172554752.0000
Epoch [7210/10000], Loss: 19180204032.0000
Epoch [7220/10000], Loss: 19194804224.0000
Epoch [7230/10000], Loss: 19111843840.0000
Epoch [7240/10000], Loss: 19094339584.0000
Epoch [7250/10000], Loss: 19169361920.0000
Epoch [7260/10000], Loss: 19123433472.0000
Epoch [7270/10000], Loss: 19077253120.0000
Epoch [7280/10000], Loss: 19006824448.0000
Epoch [7290/10000], Loss: 18961547264.0000
Epoch [7300/10000], Loss: 19028400128.0000
Epoch [7310/10000], Loss: 18966929408.0000
Epoch [7320/10000], Loss: 18900688896.0000
Epoch [7330/10000], Loss: 18963290112.0000
Epoch [7340/10000], Loss: 18881114112.0000
Epoch [7350/10000], Loss: 18833551360.0000
Epoch [7360/10000], Loss: 18858723328.0000
Epoch [7370/10000], Loss: 18847524864.0000
Epoch [7380/10000], Loss: 18845157376.0000
Epoch [7390/10000], Loss: 18783512576.0000
Epoch [7400/10000], Loss: 18763503616.0000
Epoch [7410/10000], Loss: 18774749184.0000
Epoch [7420/10000], Loss: 18684508160.0000
Epoch [7430/10000], Loss: 18706425856.0000
Epoch [7440/10000], Loss: 18726985728.0000
Epoch [7450/10000], Loss: 18660884480.0000
Epoch [7460/10000], Loss: 18609545216.0000
Epoch [7470/10000], Loss: 18663884800.0000
Epoch [7480/10000], Loss: 18644033536.0000
Epoch [7490/10000], Loss: 18574614528.0000
Epoch [7500/10000], Loss: 18532057088.0000
Epoch [7510/10000], Loss: 18593206272.0000
Epoch [7520/10000], Loss: 18500268032.0000
Epoch [7530/10000], Loss: 18471202816.0000
Epoch [7540/10000], Loss: 18492487680.0000
Epoch [7550/10000], Loss: 18522370048.0000
Epoch [7560/10000], Loss: 18427199488.0000
Epoch [7570/10000], Loss: 18377887744.0000
Epoch [7580/10000], Loss: 18439983104.0000
Epoch [7590/10000], Loss: 18399823872.0000
Epoch [7600/10000], Loss: 18316818432.0000
Epoch [7610/10000], Loss: 18327015424.0000
Epoch [7620/10000], Loss: 18376284160.0000
Epoch [7630/10000], Loss: 18315929600.0000
Epoch [7640/10000], Loss: 18237655040.0000
Epoch [7650/10000], Loss: 18266791936.0000
Epoch [7660/10000], Loss: 18320185344.0000
Epoch [7670/10000], Loss: 18258964480.0000
Epoch [7680/10000], Loss: 18192740352.0000
Epoch [7690/10000], Loss: 18158239744.0000
Epoch [7700/10000], Loss: 18181695488.0000
Epoch [7710/10000], Loss: 18181761024.0000
Epoch [7720/10000], Loss: 18080423936.0000
Epoch [7730/10000], Loss: 18158579712.0000
Epoch [7740/10000], Loss: 18100051968.0000
Epoch [7750/10000], Loss: 18035136512.0000
Epoch [7760/10000], Loss: 18030438400.0000
Epoch [7770/10000], Loss: 18113280000.0000
Epoch [7780/10000], Loss: 18066647040.0000
Epoch [7790/10000], Loss: 18000637952.0000
Epoch [7800/10000], Loss: 17934180352.0000
Epoch [7810/10000], Loss: 18031814656.0000
Epoch [7820/10000], Loss: 17979893760.0000
Epoch [7830/10000], Loss: 17896286208.0000
Epoch [7840/10000], Loss: 17868812288.0000
Epoch [7850/10000], Loss: 17932695552.0000
Epoch [7860/10000], Loss: 17895813120.0000
Epoch [7870/10000], Loss: 17815005184.0000
Epoch [7880/10000], Loss: 17793396736.0000
Epoch [7890/10000], Loss: 17829416960.0000
Epoch [7900/10000], Loss: 17849985024.0000
Epoch [7910/10000], Loss: 17754613760.0000
Epoch [7920/10000], Loss: 17734287360.0000
Epoch [7930/10000], Loss: 17839464448.0000
Epoch [7940/10000], Loss: 17740017664.0000
Epoch [7950/10000], Loss: 17682644992.0000
Epoch [7960/10000], Loss: 17683396608.0000
Epoch [7970/10000], Loss: 17688461312.0000
Epoch [7980/10000], Loss: 17609519104.0000
Epoch [7990/10000], Loss: 17693644800.0000
Epoch [8000/10000], Loss: 17677570048.0000
Epoch [8010/10000], Loss: 17598138368.0000
Epoch [8020/10000], Loss: 17534072832.0000
Epoch [8030/10000], Loss: 17622708224.0000
Epoch [8040/10000], Loss: 17575421952.0000
Epoch [8050/10000], Loss: 17504624640.0000
Epoch [8060/10000], Loss: 17505593344.0000
Epoch [8070/10000], Loss: 17522780160.0000
Epoch [8080/10000], Loss: 17429184512.0000
Epoch [8090/10000], Loss: 17424078848.0000
Epoch [8100/10000], Loss: 17506009088.0000
Epoch [8110/10000], Loss: 17373241344.0000
Epoch [8120/10000], Loss: 17429035008.0000
Epoch [8130/10000], Loss: 17420546048.0000
Epoch [8140/10000], Loss: 17318205440.0000
Epoch [8150/10000], Loss: 17383505920.0000
Epoch [8160/10000], Loss: 17356316672.0000
Epoch [8170/10000], Loss: 17270130688.0000
Epoch [8180/10000], Loss: 17338884096.0000
Epoch [8190/10000], Loss: 17327214592.0000
Epoch [8200/10000], Loss: 17279463424.0000
Epoch [8210/10000], Loss: 17206632448.0000
Epoch [8220/10000], Loss: 17262927872.0000
Epoch [8230/10000], Loss: 17165797376.0000
Epoch [8240/10000], Loss: 17193099264.0000
Epoch [8250/10000], Loss: 17237813248.0000
Epoch [8260/10000], Loss: 17145164800.0000
Epoch [8270/10000], Loss: 17097780224.0000
Epoch [8280/10000], Loss: 17155079168.0000
Epoch [8290/10000], Loss: 17132945408.0000
Epoch [8300/10000], Loss: 17036755968.0000
Epoch [8310/10000], Loss: 17115918336.0000
Epoch [8320/10000], Loss: 17099726848.0000
Epoch [8330/10000], Loss: 17004758016.0000
Epoch [8340/10000], Loss: 16995623936.0000
Epoch [8350/10000], Loss: 17025379328.0000
Epoch [8360/10000], Loss: 17042255872.0000
Epoch [8370/10000], Loss: 16924684288.0000
Epoch [8380/10000], Loss: 16950146048.0000
Epoch [8390/10000], Loss: 17024071680.0000
Epoch [8400/10000], Loss: 16905218048.0000
Epoch [8410/10000], Loss: 16875421696.0000
Epoch [8420/10000], Loss: 16981414912.0000
Epoch [8430/10000], Loss: 16891516928.0000
Epoch [8440/10000], Loss: 16805768192.0000
Epoch [8450/10000], Loss: 16848031744.0000
Epoch [8460/10000], Loss: 16894860288.0000
Epoch [8470/10000], Loss: 16858976256.0000
Epoch [8480/10000], Loss: 16758952960.0000
Epoch [8490/10000], Loss: 16730971136.0000
Epoch [8500/10000], Loss: 16786704384.0000
Epoch [8510/10000], Loss: 16795893760.0000
Epoch [8520/10000], Loss: 16683686912.0000
Epoch [8530/10000], Loss: 16702092288.0000
Epoch [8540/10000], Loss: 16763962368.0000
Epoch [8550/10000], Loss: 16683048960.0000
Epoch [8560/10000], Loss: 16645136384.0000
Epoch [8570/10000], Loss: 16750691328.0000
Epoch [8580/10000], Loss: 16652770304.0000
Epoch [8590/10000], Loss: 16577718272.0000
Epoch [8600/10000], Loss: 16621923328.0000
Epoch [8610/10000], Loss: 16633239552.0000
Epoch [8620/10000], Loss: 16540891136.0000
Epoch [8630/10000], Loss: 16578623488.0000
Epoch [8640/10000], Loss: 16655206400.0000
Epoch [8650/10000], Loss: 16556931072.0000
Epoch [8660/10000], Loss: 16465077248.0000
Epoch [8670/10000], Loss: 16632245248.0000
Epoch [8680/10000], Loss: 16548523008.0000
Epoch [8690/10000], Loss: 16435972096.0000
Epoch [8700/10000], Loss: 16439989248.0000
Epoch [8710/10000], Loss: 16502726656.0000
Epoch [8720/10000], Loss: 16405437440.0000
Epoch [8730/10000], Loss: 16448935936.0000
Epoch [8740/10000], Loss: 16401833984.0000
Epoch [8750/10000], Loss: 16334807040.0000
Epoch [8760/10000], Loss: 16368381952.0000
Epoch [8770/10000], Loss: 16473218048.0000
Epoch [8780/10000], Loss: 16374027264.0000
Epoch [8790/10000], Loss: 16282378240.0000
Epoch [8800/10000], Loss: 16293383168.0000
Epoch [8810/10000], Loss: 16429017088.0000
Epoch [8820/10000], Loss: 16278544384.0000
Epoch [8830/10000], Loss: 16236674048.0000
Epoch [8840/10000], Loss: 16370742272.0000
Epoch [8850/10000], Loss: 16204353536.0000
Epoch [8860/10000], Loss: 16282034176.0000
Epoch [8870/10000], Loss: 16165651456.0000
Epoch [8880/10000], Loss: 16345307136.0000
Epoch [8890/10000], Loss: 16181713920.0000
Epoch [8900/10000], Loss: 16144455680.0000
Epoch [8910/10000], Loss: 16199261184.0000
Epoch [8920/10000], Loss: 16226864128.0000
Epoch [8930/10000], Loss: 16151510016.0000
Epoch [8940/10000], Loss: 16069234688.0000
Epoch [8950/10000], Loss: 16221099008.0000
Epoch [8960/10000], Loss: 16138140672.0000
Epoch [8970/10000], Loss: 16031289344.0000
Epoch [8980/10000], Loss: 16076396544.0000
Epoch [8990/10000], Loss: 16126156800.0000
Epoch [9000/10000], Loss: 16023005184.0000
Epoch [9010/10000], Loss: 16007345152.0000
Epoch [9020/10000], Loss: 16181982208.0000
Epoch [9030/10000], Loss: 16084757504.0000
Epoch [9040/10000], Loss: 16001732608.0000
Epoch [9050/10000], Loss: 15942478848.0000
Epoch [9060/10000], Loss: 15951780864.0000
Epoch [9070/10000], Loss: 15944798208.0000
Epoch [9080/10000], Loss: 15896205312.0000
Epoch [9090/10000], Loss: 15997906944.0000
Epoch [9100/10000], Loss: 15852871680.0000
Epoch [9110/10000], Loss: 15904259072.0000
Epoch [9120/10000], Loss: 15992311808.0000
Epoch [9130/10000], Loss: 15935448064.0000
Epoch [9140/10000], Loss: 15839268864.0000
Epoch [9150/10000], Loss: 15783864320.0000
Epoch [9160/10000], Loss: 15958487040.0000
Epoch [9170/10000], Loss: 15860670464.0000
Epoch [9180/10000], Loss: 15783315456.0000
Epoch [9190/10000], Loss: 15734597632.0000
Epoch [9200/10000], Loss: 15819678720.0000
Epoch [9210/10000], Loss: 15746620416.0000
Epoch [9220/10000], Loss: 15719409664.0000
Epoch [9230/10000], Loss: 15812999168.0000
Epoch [9240/10000], Loss: 15751278592.0000
Epoch [9250/10000], Loss: 15644568576.0000
Epoch [9260/10000], Loss: 15733157888.0000
Epoch [9270/10000], Loss: 15724306432.0000
Epoch [9280/10000], Loss: 15617004544.0000
Epoch [9290/10000], Loss: 15731532800.0000
Epoch [9300/10000], Loss: 15657965568.0000
Epoch [9310/10000], Loss: 15581690880.0000
Epoch [9320/10000], Loss: 15687882752.0000
Epoch [9330/10000], Loss: 15626765312.0000
Epoch [9340/10000], Loss: 15538247680.0000
Epoch [9350/10000], Loss: 15622797312.0000
Epoch [9360/10000], Loss: 15562005504.0000
Epoch [9370/10000], Loss: 15501617152.0000
Epoch [9380/10000], Loss: 15615681536.0000
Epoch [9390/10000], Loss: 15465839616.0000
Epoch [9400/10000], Loss: 15553048576.0000
Epoch [9410/10000], Loss: 15618019328.0000
Epoch [9420/10000], Loss: 15516972032.0000
Epoch [9430/10000], Loss: 15428354048.0000
Epoch [9440/10000], Loss: 15442135040.0000
Epoch [9450/10000], Loss: 15511350272.0000
Epoch [9460/10000], Loss: 15395200000.0000
Epoch [9470/10000], Loss: 15453029376.0000
Epoch [9480/10000], Loss: 15446786048.0000
Epoch [9490/10000], Loss: 15334318080.0000
Epoch [9500/10000], Loss: 15462760448.0000
Epoch [9510/10000], Loss: 15401046016.0000
Epoch [9520/10000], Loss: 15304540160.0000
Epoch [9530/10000], Loss: 15434773504.0000
Epoch [9540/10000], Loss: 15322351616.0000
Epoch [9550/10000], Loss: 15294841856.0000
Epoch [9560/10000], Loss: 15414770688.0000
Epoch [9570/10000], Loss: 15289768960.0000
Epoch [9580/10000], Loss: 15251183616.0000
Epoch [9590/10000], Loss: 15320202240.0000
Epoch [9600/10000], Loss: 15263808512.0000
Epoch [9610/10000], Loss: 15206699008.0000
Epoch [9620/10000], Loss: 15306333184.0000
Epoch [9630/10000], Loss: 15167053824.0000
Epoch [9640/10000], Loss: 15350538240.0000
Epoch [9650/10000], Loss: 15247004672.0000
Epoch [9660/10000], Loss: 15136593920.0000
Epoch [9670/10000], Loss: 15176950784.0000
Epoch [9680/10000], Loss: 15243730944.0000
Epoch [9690/10000], Loss: 15197547520.0000
Epoch [9700/10000], Loss: 15077328896.0000
Epoch [9710/10000], Loss: 15165659136.0000
Epoch [9720/10000], Loss: 15182614528.0000
Epoch [9730/10000], Loss: 15040357376.0000
Epoch [9740/10000], Loss: 15124745216.0000
Epoch [9750/10000], Loss: 15145594880.0000
Epoch [9760/10000], Loss: 15004985344.0000
Epoch [9770/10000], Loss: 15112262656.0000
Epoch [9780/10000], Loss: 15043771392.0000
Epoch [9790/10000], Loss: 15015484416.0000
Epoch [9800/10000], Loss: 15173045248.0000
Epoch [9810/10000], Loss: 15010365440.0000
Epoch [9820/10000], Loss: 14946551808.0000
Epoch [9830/10000], Loss: 15003002880.0000
Epoch [9840/10000], Loss: 15035953152.0000
Epoch [9850/10000], Loss: 14918465536.0000
Epoch [9860/10000], Loss: 14948540416.0000
Epoch [9870/10000], Loss: 14975939584.0000
Epoch [9880/10000], Loss: 14882556928.0000
Epoch [9890/10000], Loss: 14960998400.0000
Epoch [9900/10000], Loss: 14955343872.0000
Epoch [9910/10000], Loss: 14840415232.0000
Epoch [9920/10000], Loss: 14979625984.0000
Epoch [9930/10000], Loss: 14938395648.0000
Epoch [9940/10000], Loss: 14787784704.0000
Epoch [9950/10000], Loss: 14946582528.0000
Epoch [9960/10000], Loss: 14896962560.0000
Epoch [9970/10000], Loss: 14750309376.0000
Epoch [9980/10000], Loss: 14930928640.0000
Epoch [9990/10000], Loss: 14782153728.0000
Epoch [10000/10000], Loss: 14777547776.0000
Test Loss: 57464336384.0000
Training time: 23.42 seconds

As can be seen we can achieve a similar magnitude in test loss but using far fewer features and thus speeding up inference time

The test loss may seem extremely large but this is mostly because of the large size of the testing set and the fact that house prices are also fairly large (of the magnitude 10^6) and thus even the squares of small errors accumulate quickly and lead to a large final loss

Conclusion¶

As we can see various factors such as square feet, view, zipcode and more are often found in housing listings. However through data analysis we can identify which features truly matter to consumers (such as square feet, location in the form of zipcode, whether the house has a basement or not, etc.).

Using this data we can narrow down which features are best analyzed when modelling the price of housing using ML techniques.